Ricardo Gallegos-Hernandez, federal prisoner # 36299-013, an alien with a detainer placed against him, proceeding pro se and in forma pauperis, challenges the denial of his 28 U.S.C. § 2241 petition seeking the benefit of drug-rehabilitation programs and halfway house placement. The district court dismissed the action for lack of subject-matter jurisdiction under § 2241 on grounds that the asserted claims should have been brought under 42 U.S.C. § 1983. In the alternative, the district court held the case should be dismissed because Gallegos had failed to exhaust his administrative remedies. Finally, the court alternatively held, with respect to the merits, that Gallegos had failed to state a claim for the denial of any constitutional right. Gallegos argues that his claim was properly brought under § 2241; that he was not required to exhaust his administrative remedies; that his exclusion from the program violated his due process rights; and, finally, that his exclu[*193] sion violated his equal protection rights. We hold that the district court erred in dismissing Gallegos’s claim for lack of jurisdiction and hold that Gallegos’s claim is properly brought under § 2241. We also hold that the district court, in its alternative denial of relief, further erred in requiring Gallegos to exhaust his administrative remedies. We ultimately AFFIRM the district court’s judgment dismissing Gallegos’s petition on its merits for failure to state a claim for the denial of any constitutional right.

I.

Gallegos, a native of Mexico, was convicted of illegal reentry in violation of 8 U.S.C. § 1326(a) and (b)(2). He was sentenced to 48 months of imprisonment. Immigration and Customs Enforcement (ICE) issued a detainer against him under 8 U.S.C. § 1231(a)(5) based on its determination that he is subject to immediate removal from the United States upon his release from Bureau of Prisons’ (BOP) custody.

Gallegos has filed a habeas petition under 28 U.S.C. § 2241, asserting that the BOP improperly denied him benefits and opportunities made available under 18 U.S.C. §§ 3621 and 3624 on the basis that he is not a U.S. citizen. Sections 3621 and 3624 involve drug treatment and other rehabilitation programs, which, if completed, offer prisoners potential reductions in sentence up to 12 months. Placement in community-based reentry facilities (i.e., halfway houses) is a component of these programs. 28 C.F.R. § 550.53(a)(1)-(3). The BOP has, however, exercised its discretion to exclude ICE detainees from eligibility for early release and participation in the community-based treatment programs because of the flight risk associated with such prisoners. 28 C.F.R. § 550.55(b)(1). In his petition, Gallegos challenged the constitutionality of these exclusions. He further maintained that exhaustion of his administrative remedies would be futile because these constitutional claims could not be addressed administratively.

The district court dismissed the petition for lack of subject-matter jurisdiction under § 2241, as it determined the claims did not “impact the fact or duration” of his sentence. The court concluded that the claims should have been brought under 42 U.S.C. § 1983. The district court also gave alternative reasons that the petition had no merit: the petition should be dismissed for Gallegos’s failure to exhaust his administrative remedies; the petition should be denied because Gallegos has no liberty interest in early release to support a due-process claim; and, he has no equal-protection right to placement in a particular penal institution. This appeal followed. It is one of approximately 50 similar appeals pending before our court, in the sense that this appeal challenges the BOP’s denial of the drug rehabilitation and halfway house programs to inmates who have detainers placed on them.

II.

In challenging the denial and dismissal of his § 2241 petition, Gallegos argues that the district court had subject-matter jurisdiction because § 2241 is the proper procedural vehicle for his claims; that he was not required to exhaust his administrative remedies; that he has a liberty interest in rehabilitation and placement in a halfway house; and, finally that his equal protection rights were violated by denying him these benefits on grounds that he is an alien.

Our court reviews a dismissal for lack of subject-matter jurisdiction de novo. Williams v. Dallas Area Rapid Transit, [*194] 242 F.3d 315, 318 (5th Cir.2001). We review for abuse of discretion a dismissal of a § 2241 petition for failure to exhaust administrative remedies. Fuller v. Rich, 11 F.3d 61, 62 (5th Cir.1994). “In an appeal from the denial of habeas relief, this court reviews a district court’s findings of fact for clear error and issues of law de novo.” Jeffers v. Chandler, 253 F.3d 827, 830 (5th Cir.2001).

A.

We begin by addressing the jurisdictional ruling upon which the district court based its dismissal. Section 2241 is the proper procedural vehicle if a prisoner “challenges the execution of his sentence rather than the validity of his conviction and sentence.” United States v. Cleto, 956 F.2d 83, 84 (5th Cir.1992).

Here, Gallegos maintains he is being denied benefits that could result in a one-year reduction in his sentence. As we have noted, participation in the rehabilitation program can result in a reduction in sentence of up to twelve months. A claim challenging the denial of entry into the program therefore is properly raised under § 2241 and the district court erred in concluding it lacked subject-matter jurisdiction of Gallegos’s § 2241 petition. See Cenante v. United States, 402 Fed.Appx. 886, 887 (5th Cir.2010) (court had subject-matter jurisdiction over § 2241 claim seeking admission into drug rehabilitation program); see also Rublee v. Fleming, 160 F.3d 213, 214-17 (5th Cir.1998); Canajal v. Tombone, 31 Fed.Appx. 155 (5th Cir.2001).

B.

Now that we have determined that the district court had jurisdiction to consider the claims, we must address the alternative rulings on the merits of the claims because they are now at issue. We thus turn to the question of whether Gallegos was required to exhaust his administrative remedies. We have held that a federal prisoner filing a § 2241 petition must first pursue all available administrative remedies. See Rourke v. Thompson, 11 F.3d 47, 49 (5th Cir.1993). However, “[ejxceptions to the exhaustion requirement are appropriate where the available administrative remedies either are unavailable or wholly inappropriate to the relief sought, or where the attempt to exhaust such remedies would itself be a patently futile course of action.” Fuller, 11 F.3d at 62.

'Here, Gallegos challenges the constitutionality of the BOP regulations. His claim is not that the BOP has erred in its application of the regulation excluding alien detainees from participating in rehabilitation programs and halfway house placements. His argument is that the regulation itself must be struck from the Code of Federal Regulations because it violates the due-process and equal-protection rights, under the United States Constitution, of him and all non-citizens. Thus, it would have been futile for him to make an administrative challenge seeking this relief from those who are charged to enforce the regulation. See Taylor v. United States Treasury Dept., 127 F.3d 470, 477 (5th Cir.1997) (noting exhaustion not required where, inter alia, claimant raises constitutional claim that agency would clearly reject). Our precedent supports Gallegos’s argument and therefore we hold that the district court erred in dismissing these claims for failure to exhaust. Now that the merits of the claims are before us, we will turn to the substance of those claims.

C.

Gallegos is housed in a facility that segregates alien inmates from citizen in[*195] mates. Where he is housed, drug-rehabilitation and other related programs that could lead to early release are not available. The denial of these benefits is the basis of Gallegos’s due-process claims. The district court, however, concluded he had no liberty interest in a particular facility or in early release. Gallegos responds by contending these liberty interests arise from §§ 3621 and 3624, and, thus, the BOP policy of denying access to these opportunities to ICE detainees is arbitrary and capricious.

Section 3624(c) provides that the BOP “shall, to the extent practicable” afford prisoners an opportunity to prepare for reentry to the community. Gallegos seizes on the word “shall” as creating a liberty interest in these programs and opportunities. Our court, however, explained in Richardson v. Joslin, 501 F.3d 415 (5th Cir.2007), that “[t]he hallmark of a statute that has not created a liberty interest is discretion,” and “[w]here the statute grants the prison administration discretion, the government has conferred no right on the inmate.” Id. at 419 (emphasis added). As evidenced by the phrase “to the extent practicable” and the employment of “individual basis” review of eligibility provided in the regulations, the BOP has discretion whether to grant the benefits. See 28 C.F.R. § 570.22. Consequently, there is no right conferred here. Furthermore, our court has explained that § 3624 does not impinge on the BOP’s authority to determine the facility in which a prisoner should be housed. United States v. Sneed, 63 F.3d 381, 388 n. 6 (5th Cir.1995); see also Tighe v. Wall, 100 F.3d 41, 42 (5th Cir.1996). As such, there is no liberty interest in a particular facility— including one wherein drug-rehabilitation programs are available — created by § 3624.

Section 3621 provides that the BOP “shall” provide residential substance abuse treatment to prisoners with treatable addictions and shall offer early release as a potential incentive to complete the program. See § 3621(b) and (e)(2)(B). But this statute does not create a liberty interest in early release. As we have explained in Rublee, 160 F.3d at 216, § 3621(e)(2)(B) affords the BOP discretion in deciding whether to allow early release. Id. at 217. Because neither statute creates a liberty interest in the benefits Gallegos claims, his due-process claims fail.

D.

Gallegos further contends that denial of rehabilitation benefits on the basis of his status as a non-citizen prisoner violates his equal-protection rights. To establish an equal protection claim, Gallegos must show that two or more classifications of similarly situated persons were treated differently. See Stefanoff v. Hays County, Tex., 154 F.3d 523, 525-26 (5th Cir.1998). Once this element is established, the court must then determine the appropriate level of scrutiny. Id. at 525. “[S]trict scrutiny is appropriate only where a government classification implicates a suspect class or a fundamental right.” Rublee, 160 F.3d at 217. “Otherwise, rational-basis review applies and this court need only determine whether the classification is rationally related to a legitimate government interest.” Id.

As other circuits have recognized, alien prisoners with ICE detainers, such as Gallegos, cannot show that exclusion from rehabilitation programs, or from halfway house placement, establishes that alien prisoners, as an identifiable group, are being treated differently from other similarly situated prisoners who are not aliens. See McLean v. Crabtree, 173 F.3d 1176, 1185 (9th Cir.1999). This is true

[*196] because, on its face, the statute and regulations classify prisoners — not as aliens and non-aliens — but as those who have ICE detainers against them and those who do not. Id. Gallegos points to no evidence that the exclusion is motivated by discriminatory intent against aliens. Instead, Gallegos has only shown that the BOP regulations require “prisoners with detainers being treated differently from prisoners without detainers.” Id.

The Third Circuit also supports this reasoning as it found identical claims — ICE detainees seeking to participate in rehabilitative and early-release programs excluded solely on the basis of their having ICE detainers lodged against them — without merit because the class of ineligible prisoners included non-aliens as well as aliens. Adams v. Apker, 148 Fed.Appx. 93, 95-96 (3d Cir.2005); see also 28 C.F.R. § 550.55(b) (listing inmates not eligible for early release); P.S. 7310.04, pp. 10-11 (listing inmates not ordinarily eligible for halfway house placement).

In any event, this claim survives rational-basis review. Rational-basis review is appropriate because the classification of prisoners based on whether they have ICE detainers is not a suspect classification. Carvajal, 31 Fed.Appx. at 155. Nor does this claim involve a fundamental right. See Wottlin v. Fleming, 136 F.3d 1032, 1036-37 (5th Cir.1998); see also Torres v. Chapman, 359 Fed.Appx. 459, 462 (5th Cir.2009) (“Our precedent establishes that the ... opportunity to obtain a reduced sentence [under § 3621] is not a fundamental right.”). Applying rational-basis review, our court has previously held that the determination that ICE detainees are ineligible to participate in prerelease halfway house confinement is rationally related to preventing those detainees from fleeing during the community-based portion of those programs. Carvajal, 31 Fed. Appx. at 155. This reasoning is supported by that of other circuits. See McLean, 173 F.3d at 1186 (“Excluding prisoners with detainers from participating in the community-based treatment programs, and consequently from sentence reduction eligibility, is at least rationally related to the BOP’s legitimate interest in preventing prisoners from fleeing detainers while participating in community treatment programs.”). Thus, Gallegos’s equal-protection claims fail.

III.

We sum up: The district court erred in its conclusion that it lacked subject-matter jurisdiction over Gallegos’s claims under 28 U.S.C. § 2241. We hold that § 2241 is indeed the proper procedural vehicle for Gallegos’s claims. In its alternative holding, the district court also erred in dismissing the complaint for failure to exhaust his administrative remedies. Because Gallegos raised the constitutionality of the statutes and regulations, exhaustion before the administrative agency would have been futile. Finally, the district court correctly concluded that Gallegos failed to establish a denial of his due-process or equal-protection rights.

For the foregoing reasons, the judgment of the district court is

AFFIRMED.