Bale the second actor to decline the role after Leonardo DiCaprio discussed the part with "Slumdog Millionaire" director Danny Boyle, but no deal was reached, according to industry journal Variety.
The Oscar-winning star had conflicting feelings about the role, and concluded that he simply wasn't right for it, sources told the Hollywood Reporter.
Oscar-winning screenwriter Aaron Sorkin announced last month that Bale had been chosen for the role. "We needed the best actor on the board in a certain age range and that's Chris Bale," he told Bloomberg Television.
"He didn't have to audition," said Sorkin, although the writer said "there was a meeting" before the British-born actor was given the part.
Sony Pictures is in discussions with US comic actor Seth Rogen to play Apple co-founder Steve Wozniak, according to Variety.
Bale received a best supporting actor Oscar in 2011 for his role in "The Fighter," in which he plays the older brother of a washed-up boxer struggling to revive his career.
The actor had a breakout performance as the lead actor in the 2000 movie "American Psycho," and also earned a lead actor Oscar nomination for his turn in last year's "American Hustle."