According to The Wrap, the actor's deal with 20th Century Fox "is in jeopardy of falling apart".
Speaking to Digital Spy recently, Tatum said he had been working on his accent as the card-throwing Cajun.
It's also not clear what the actor's departure would mean for his producing partner Reid Carolin.
Tatum appeared with the entire X-Men cast as recently as two weekends ago at Fox's Comic-Con panel in San Diego.
#auniverseunited pic.twitter.com/cFqkJw92Zb
— Channing Tatum (@channingtatum) July 15, 2015
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It is thought that Tatum's desire to move into directing soon is playing a part in his potential Gambit exit.
Casting is currently under way on the comic book movie, with Spectre's Léa Seydoux said to be testing for the female lead. The blockbuster is due to go into production this October with a hefty $154 million budget.
The X-Men spinoff is being directed by Rupert Wyatt and is set for release on October 7, 2016.
Taylor Kitsch originally played the smooth-talking New Orleans-born mutant in X-Men Origins: Wolverine.
It is expected that this new version of Gambit will eventually join the main X-Men movies down the road.
