The filmmaking duo - who hail from Boston themselves - are tipped to direct and star, alongside Ben's brother Casey Affleck.
"We're doing a Whitey Bulger movie. Warner's got it for us," Matt told US GQ.
"There are a couple of competing movies and I don't think it's been announced yet that we're doing it. But the sooner it's announced the better, just because everyone else will back off, hopefully. I'm really excited about it."
The drama is still in early stages, with no word as to who would play Whitey, although Matt already has some ideas.
"If it's a straight biopic, we'll do it over a period of time. But it's always a question of what part of the story do you tell, and biopics are always a little cumbersome. So do we find another way in? We're still figuring it out," he explained.
As the leader of the notorious Winter Hill gang in Boston, Bulger - who was on the FBI's top ten Most Wanted list for a few decades - was finally arrested after years of hiding in California.
His life story is the subject of three other projects in production. Twilight actor Peter Facinelli is producing an adaptation of Edward MacKenzie and Phyllis Karas' book, Street Soldier: My Life As An Enforcer For Whitey Bulger And The Boston Irish Mob. There is another being made about the gang's chief enforcer John Martorano, and Black Mass, which focuses on the relationship between the FBI and the mob, is also in the pipeline.