Cooper was rumoured in August to be in talks to play a mentor-turned-love interest for Beyoncé's rising music star in the upcoming movie.
The actor downplayed the likelihood of his casting in A Star is Born at the Hollywood premiere of his new film The Worlds.
"[It was] just a rumour," Cooper told E! News.
Cooper further explained that while he believes Eastwood is "one of the best directors alive", he's not sure the project is a good idea.
"There are like three versions already [of A Star is Born]," he noted.
The original A Star is Born was released in 1937 and starred Janet Gaynor and Frederic March.
A 1954 remake paired Judy Garland and James Mason, with Barbra Streisand and Kris Kristofferson updating A Star is Born 22 years later.
Beyoncé confirmed her casting in Eastwood's A Star is Born last summer, saying at the time that she was "so honoured" to win the starring role.