The pair could reunite, according to The Hollywood Reporter, after working together in 2000 on The Beach.
The movie is the second about the late Apple co-founder, who died in 2011 at the age of 56 after suffering from pancreatic cancer.
Last year, Two And A Half Men star Ashton Kutcher played the title role in the movie Jobs.
According to The Hollywood Reporter, Sony Pictures is in talks with Boyle about directing the new film and the Slumdog Millionaire filmmaker wants DiCaprio to star.
David Fincher, who directed Facebook film The Social Network, was originally linked to the project.
British director Boyle recently enjoyed acclaim for his role presiding over the opening ceremony of the 2012 Olympic Games.
He is next tipped to make Porno, the sequel to cult film Trainspotting, while The Wolf Of Wall Street heartthrob DiCaprio is set to star in The Revenant.
Aaron Sorkin penned the new biopic on the late technology innovator, based on Walter Isaacson’s best-selling biography.
Fincher allegedly quit the project over a pay row.
Sony Pictures is in talks with Boyle while the acclaimed director is said to have already approached DiCaprio, as a replacement for Christian Bale, who Fincher had in mind.
Last week reports emerged that Fincher walked out on the film over his demands for $10 million (€7.25m) in up-front wages and control of the film marketing.