New rumours emerged this week amid reports that Bond producer Barbara Broccoli said it was now "time" for a black actor to take the role.
This story first appeared in the New York Post and is republished with permission.
Craig will reprise the role of the spy with the licence to kill for the 25th film in the franchise, which will be directed by Danny Boyle.
Idris Elba has ignited hopes of fans that he could be the next James Bond by releasing a cryptic tweet, following a warning "not to believe the hype".
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We come to you today with the latest via Luther star Idris Elba.
Following the announcement that current Bond Daniel Craig would step aside, rumours have been rife that Elba would take over the role, but nothing was confirmed. "My name is Elba, Idris Elba".
The actor posted a selfie alongside an obvious nod to 007's iconic line: "The name's Bond, James Bond".
Reaching very, very far for a connection, one fan commented: "I see two clocks in the picture". You need a guy with a physically strong presence.
A representative for Fuqua told THR, "He never had a conversation with Barbara about the franchise or about any casting".