The first-time director tells Variety he had someone else in mind for the part before Lady GaGa signed on, but he refused to name names, revealing only that studio bosses "wouldn't make the movie" with his pick.
Cooper and White reportedly met, but it's not clear whether that was to talk about the role of Jackson or as the film's music consultant - a job that went to Willie Nelson's songwriter son Lukas.
Cooper was previously offered the role of Maine by pal Clint Eastwood, when he was on board the project as director, but the veteran moviemaker's "American Sniper" star turned him down because he didn't think he was old enough to portray a grizzled, alcoholic rock star.
The first-time director eventually decided to play his own leading man opposite Lady GaGa, and their film has become a huge hit, sparking Oscar buzz, particularly for their song "Shallow", which many critics feel should pick up Best Song at the Academy Awards next year.
Cooper tells Variety he's well aware it's an Oscar-worthy song and he'd love to sing it onstage at the Dolby Theater next year.
"We talked about that actually, because I'm such a maniac," the actor/director says. "I started texting her (GaGa) the whole pitch of how we should do it. So we'll see. There might be a cool, unorthodox way we could perform it."