The 39 year-old actor has been approached by Boyle, who is in negotiations to replace David Fincher as director.
Fincher was previously attached to direct the film, with rumours that he wanted Christian Bale to play Steve Jobs, reported the Huffington Post.
The movie is expected to focus on the launches of Apple's original Macintosh computer (1984), NeXT Cube (1990), and original iPod (2001).
It is said to be produced by Scott Rudin and written by Aaron Sorkin (The Social Network), based on the best-selling biography of Jobs by Walter Isaacson.
If Boyle and Leonardo DiCaprio sign on to the project, it will be the first time they have collaborated since 2000's thriller 'The Beach', but it will be both the actor and director's first time working with Sorkin.