The Social Network's Aaron Sorkin has written the screenplay for the untitled movie, which will be based on Walter Isaacson's book about the Apple co-founder, and the filmmaker recently met with Sony executives to talk about boarding the film as director.
However, Fincher has insisted he will only direct the film if Bale agrees to lead the cast, according to The Wrap.com.
Bale is currently not attached to the film and has not taken any meetings about it, but producers are hoping to begin shooting next year (15).
If he signs on, The Dark Knight star will become the second actor to portray the late innovator after Ashton Kutcher starred in Jobs last year (13).
Sony executives and Bale's representatives have not commented on the news.