Boyle told the Radio Times the refusal left he and screenwriter Frank Cottrell Boyce "in grief".
He wanted his film about Apple co-founder Steve Jobs to "fill the space in my heart left by the abandoned Bowie script", he added.
Boyle said Bowie's decision made him determined to get the Jobs film made.
The new film, with a screenplay by The West Wing's Aaron Sorkin, stars Michael Fassbender and Kate Winslet, has been tipped for Oscars success.
Meanwhile, Boyle is set to revisit his 1996 breakthrough cult hit Trainspotting, and he is hoping that the second instalment will coincide with the film's 20th anniversary next year.
He told the Radio Times: "It's not called Porno!", in reference to the Irvine Welsh novel of the same name, on which it is loosely based.
"It's T2 for now. We've got a window for the original cast to shoot in spring 2016 and hopefully it will come out the same year, on the anniversary."
Danny Boyle has spoken of his disappointment after David Bowie refused to let the director use his music for a film project.