The actress shot to fame with her role in 1984 comedy adventure movie Romancing the Stone, and she soon attracted the attention of Tinseltown's leading Lotharios.
Her co-star Douglas was determined to charm her into bed but he faced tough competition from Beatty and Nicholson, who also tried to woo her.
However, Turner refused the advances of all three men, and admits 30 years on that she is glad she avoided becoming their plaything.
She tells British magazine Style, "I knew I became a target instantly. Suddenly, there was this competition between Warren Beatty and Michael Douglas and Jack Nicholson... None of them (won). I just got on a plane and went back to New York. Honestly, living in New York probably saved me from a whole lot of rubbish."
Asked if she was not even tempted to get involved with Beatty, she adds, "Somebody who's more beautiful than me - or thinks they are? No. I don't need that c**p."