Steven Gerrard has been working to strengthen his Rangers squad as the Gers aim to stop rivals Celtic from retaining the Scottish title and Belkebla has been linked with a move to Ibrox.
Lens were also interested in the Algeria international, but Belkebla has committed himself to Brest.
He has signed a new contract to extend his stay with the Ligue 1 club until the summer of 2023.
Belkebla made 23 appearances for Brest in Ligue 1 last season and the midfielder won plaudits for his performances in the centre of the park.
Keeping him at the club is a big boost for Brest as they kick on into the new French season.
He helped Brest to a finish of 14th in the curtailed Ligue 1 campaign.
In the new season, Brest sit bottom of the table after suffering defeat in their opening two games against Nimes and Marseille, respectively.
