The 42-year-old actor, who is directing and starring in the forthcoming movie, said on Friday's episode of The Ellen DeGeneres Show that he was blown away by Lady Gaga's talent while filming the remake.
"She's unbelievable," Cooper gushed of the 31-year-old singer. "Oh my God, she's unbelievable. She really is incredible."
"It's so hard to sing," he said. "I've really been awakened to the phenomenon of singing. I just hope I can be believable enough so that you can watch Stefani -- that's her name, Gaga -- just shine, because she's incredible."
A Star is Born follows aspiring performer Ally (Lady Gaga) and the veteran entertainer (Cooper) who helps her break into the industry. The original movie opened in 1937 and was last remade in 1976 with Barbra Streisand and Kris Kristofferson.
"It's all original music," Cooper said of his version.
A Star is Born, which marks Lady Gaga's first film role and Cooper's directorial debut, opens in theaters Sept. 28, 2018. Lady Gaga, who use her legal name, Stefani Germanotta, in the movie's credits, shared a first photo from the project in April.
"I am so excited to star in my first movie alongside someone I'm so lucky to call my friend," she said. "The story of 'A Star is Born' is so special and I'm so grateful to Bradley for making my dream come true."