Watch: Barbra Streisand had other ideas for the remake of A Star Is Born
The 79-year-old musician and actor starred in the 1976 version of the film about an undiscovered singer's rise to fame with the help of a self-destructive rocker - played by Kris Kristofferson.
Streisand told Australian TV show The Sunday Project: "At first, when I heard it was going to be done again, it was supposed to be Will Smith and Beyonce, and I thought, that's interesting.
"Really make it different again, different kind of music, integrated actors, I thought that was a great idea. So, I was surprised when I saw how alike it was to the version that I did in 1976."
Gaga and Cooper's version of A Star Is Born was nominated for eight Oscars and seven Baftas and went on to gross $436m (£315m) at the box office.
Streisand said she "can’t argue with success”, but added: "I don’t care so much about success as I do originality.”
Cooper and Gaga claimed while promoting the movie in 2018 that Streisand had given their remake her endorsement.
Cooper said: "She gave us a blessing. Everybody was so excited she was there. We just looked at each other and were like, 'Wow. How are we here right now?'"
Gaga added: "She was so, so kind."
But Streisand said later the same year: "I thought it was going to be very different and have a multiracial cast, and the music was going to be rap. But it's more like the movie I made."
A Star Is Born was originally made in 1937 with Janet Gaynor and Fredric March playing an aspiring actress and a Hollywood veteran, and was remade as a musical in 1954 with Judy Garland and James Mason.
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