Cooper's directorial ambitions are a matter of record – he is already attached to make Honeymoon With Harry. And he was aware of A Star Is Born's possibility thanks to his established relationship with Clint Eastwood (American Sniper), who seriously considered casting Cooper in the drama about mentoring and the often parlous nature of stardom when he was still on board to make it. It was the friendly connection they forged during that process that led Cooper to call Eastwood about taking over American Sniper (2014) when Steven Spielberg (Bridge Of Spies) left the film.
According to Deadline, the deal is far from done yet, but Cooper has been discussing the role with Gaga and more recent screen tests passed muster with executives. And he is heavily invested in all parts of the film, working as a producer and overseeing re-writes of the script with Will Fetters (Remember Me). He will likely star as the older performer who finds a new talent and nurtures her ability while becoming closer, only to find himself on the outs when she becomes more popular than he could have hoped.
So while the film is not certain to go ahead just yet, Cooper is certainly pushing to get started on it.