Cooper, who also directed the Oscar-winning film, shot down the possibility of a tour but suggested a one-night live reading and performance of the movie's songs.
"You know what I thought would be a cool thing to do, maybe one night, is do a live reading of the movie, of the script, and sing all the songs as you're reading the script. At like, the Hollywood Bowl or something," he told host Ellen DeGeneres. "That would be cool, right?"A Star is Born opened in theaters in October and won Best Original Song for "Shallow" at the Academy Awards in February. Cooper and Lady Gaga stunned with their performance of the song during the ceremony.
"It was crazy," Cooper said of the moment. "I actually wasn't nervous 'cause I worked so hard. I just worked really hard, and Lady Gaga is so supportive. But it was terrifying, absolutely, because I'm not a singer and I didn't sing before this movie."
"It just shows if you do work really hard and you're with supportive people, that you can do things you never even thought possible," he added.
Lady Gaga had denied a romance with Cooper following the intimate performance.
"Yes, people saw love and, guess what, that's what we wanted you to see," the singer said on Jimmy Kimmel Live!
"This is a love song," she explained. "From a performance perspective, it was so important to both of us that we were connected the entire time."
Cooper voices Rocket in Avengers: Endgame, which opens in theaters Friday.