Matthew Davison appeals the district court’s denial of his petition for habeas corpus relief pursuant to 28 U.S.C. § 2241. Davison challenged his conviction for possession of a nonregistered firearm, asserting that he had registered the weapon and intimating that he was subject to an illegal search and seizure. The district court denied relief, concluding that such allegations should be presented in a 28 U.S.C. § 2255 motion and that Davison had not established that he was entitled to proceed under the savings clause of § 2255(e). Before this court, Davison indicates that federal prisoners are not restricted from proceeding under § 2241. He suggests that the district court improperly made factual findings that increased the statutory maximum or minimum sentence and that because he was actually innocent of his 120-month sentence, he should be allowed to proceed under § 2241.

We review the denial of relief under § 2241 de novo. Kinder v. Purdy, 222 F.3d 209, 212 (5th Cir. 2000). “A § 2241 petition is not ... a substitute for a motion under § 2255.” Jeffers v. Chandler, 253 F.3d 827, 830 (5th Cir. 2001). If a prisoner attempts to challenge his federal sentence through a § 2241 proceeding, the petition should be either dismissed or construed as arising under § 2255. Pack v. Yusuff 218 F.3d 448, 452 (5th Cir. 2000).

A federal prisoner may attack the validity of his conviction in a § 2241 petition if he can meet the requirements of the § 2255(e) savings clause. Kinder, 222 F.3d at 212. The prisoner bears the burden of showing that the remedy under § 2255 would be “inadequate or ineffective to test the legality of his detention.” § 2255(e); Reyes-Requena v. United States, 243 F.3d 893, 901 (5th Cir. 2001). To satisfy this burden, the prisoner must establish that his claim “is based on a retroactively applicable Supreme Court decision which establishes that the petitioner may have been convicted of a nonexistent offense” and that the claim “was foreclosed by circuit law at the time when the claim *429should have been raised.” Reyes-Requena, 243 F.3d at 904.

Davison relies on Alleyne v. United States, — U.S.-, 133 S.Ct. 2151, 186 L.Ed.2d 314 (2013), in support of this argument, but that case does not establish that Davison’s claim is based on a retroactively applicable Supreme Court opinion indicating that he was convicted of a nonexistent offense. See Reyes-Requena, 243 F.3d at 904. Additionally, Davison cites McQuiggin v. Perkins, — U.S.-, 133 S.Ct. 1924, 185 L.Ed.2d 1019 (2013), which is also unavailing to him. The judgment of the district court is AFFIRMED.