The studio has an option on Craig for sequels The Girl Who Played with Fire and The Girl Who Kicked the Hornets' Nest, but the actor is asking for more money following the $1 billion success of Skyfall.
Sony is looking to cut costs on the Stieg Larsson sequel and could potentially write Craig's character Mikael Blomkvist out of the movie, says The Hollywood Reporter.
Steven Zaillian has written the script for the movie, which is described as "production-ready". The studio may need to turn to another writer if Blomkvist has to be written out of the picture.
A Craig source allegedly claimed that the 007 star hasn't started negotiations yet and is keen to return for the follow-up.
Rooney Mara is set to return as computer hacker Lisbeth Salander for both Fire and Hornets' Nest.
David Fincher could also step back into the director's chair, although the filmmaker is also circling an adaptation of Gillian Flynn's novel Gone Girl and a 20,000 Leagues Under the Sea remake.
Watch Digital Spy's interview with Rooney Mara below: