Director Rupert Wyatt recently exited the project centered on the New Orleans-based mutant, who has the power to manipulate kinetic energy and known to fight with a staff and a deck of playing cards.
The movie is set for an October 7, 2016 release.
Fox has furiously met with filmmakers to hop on board to direct the X-Men spin-off Gambit, said The Hollywood Reporter.
Liman, 50, has had a several rounds of meetings, including one that took place Thursday.
The director last helmed the well-regarded sci-fi action movie "Edge of Tomorrow", which starred Tom Cruise. He is also known for directing "Mr & Mrs Smith" and "The Bourne Identity", two massive hits, commercially and critically.
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Fox distributed 2005's Smith, while Stacey Snider, now co-chairman of Fox, was the chairman of Universal who oversaw the tumultuous making of 2002's Bourne.
Liman just wrapped "Mena", a 1980s drug cartel drama that re-teams him with Cruise and will be distributed by Universal.
Wyatt was set to direct the stand alone X-Men film, but on September 16 dropped out of the production, citing a scheduling conflict with an unnamed project.
Gambit made his first screen appearance in "X-Men Origins: Wolverine", where he was played by Friday Night Lights star Taylor Kitsch.