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Sources tell Variety that Fincher is currently in early talks to direct the untitled drama, based on the Walter Isaacson biography "Steve Jobs."
Sony acquired the rights to the best-selling book following the Apple mogul's death in 2011 and Sorkin already completed the script earlier this year.
Sorkin has publicly said the Jobs biopic will be divided into just three long scenes, each taking place in real time backstage before one of Apple's product launches.
Real time, Sorkin explained to the Daily Beast in November, "is when a half hour for you in the audience is the same as a half hour for the character on the screen. There will be no time cuts. Each of these three scenes is going to take place before a product launch-backstage before a product launch. The first one being the Mac, the second one being NeXT (after he had left Apple), and the third one being the iPod."
"It's a little like writing about the Beatles," he added. "There are so many people out there that know him and revere him."
Sony has high hopes that the untitled biopic will perform far better at the box office than Ashton Kutcher's 2013 "Jobs," which took in just $36 million worldwide - while Fincher and Sorkin's "Social Network" raked in nearly $225 million worldwide.
The studio is also betting on the fact that the movie is based on the only authorized biography that Jobs gave his blessing to before his death, and is based on hundreds of interviews with the Apple CEO and his friends and family.
Fincher, who is currently in post-production on Ben Affleck's "Gone Girl" thriller, would apparently have time in his schedule to shoot the Jobs biopic "later this year," Variety reports.
Watch Aaron Sorkin discuss more of his ideas for the film - before he finished the script - below: