The 32-year-old singer recently invited a reporter from The New York Times Magazine into her Hollywood Hills home, where she revealed a sentimental gift from her co-star turned friend.
Cooper gave Gaga a 15-foot photo of her in a still shot from the film, which hits theaters Friday.
"It was a gift from Bradley," Gaga explains. "It's the last frame of the movie. Do you know the scene?"
The scene Gaga's referring to is the big final performance number, in which her character, Ally, is all dolled up and singing, "I'll Never Love Again" on the stage of the Shrine Auditorium.
A Star Is Born marks Cooper's directorial debut, and in various interviews over the past few months, Gaga has talked extensively about how the actor didn't want her to wear any makeup for the role, in an attempt to make her look as unrecognizable as possible.
During a press conference for the film at the Venice Film Festival in August, Gaga said "being completely vulnerable and being completely bare" was "challenging."
"For most of the film, I have no makeup on my face. I remember very, very well, I walked down the stairs from my house before we filmed the screen test for A Star Is Born, and [Bradley] had a makeup wipe in his hand and he put his hand on my face and he went like this--," she mimicked wiping down her cheek. "And there was makeup. We had put just a little bit and he said, 'I want no makeup on your face.'"
"So, this vulnerability was something that he brought out in me," Gaga continued. "For someone that doesn't necessarily feel safe [being] that vulnerable all the time, it was such a special experience with him. He made you just feel so free."
Hear more on Gaga and Cooper's newfound friendship and "instant" chemistry in the video below.