Deadline reports that Steve Zaillian (Schindler's List, Gangs of New York) is currently writing the script for the second film in the Millennium trilogy for director David Fincher. Zaillian is an accomplished writer who is also currently working on The Red Riding Trilogy remakes and the new gangster flick The Irishman for Martin Scorsese.
This gives the impression production could be moving quickly on the second installment. There had been talk that the final two films in the trilogy The Girl Who Played With Fire and The Girl Who Kicked The Hornet's Nest would be shot back to back. It would make sense to shoot the two films at once to save money on production costs along with being able to keep the in-demand Daniel Craig in the lead role.
The same story brings up a new project for Fincher which has Sony looking to him to direct their new Cleopatra film which has Angelina Jolie attached in the lead. It's unlikely as it could end up conflicting with Disney's 20, 000 Leagues Under The Sea: Captain Nemo which Fincher has been involved with for a while now.
Fincher is in a unique position where he can make a passion project over a commercial studio project like Captain Nemo or Cleopatra. I wouldn't rule out Fincher moving forward with Fire and Hornet's Nest before jumping into these effects heavy and time consuming blockbusters. As the turn around time for post-production on the Millennium films would be minimal as everything is in camera and special effects would be limited.