The much-married Ms Taylor lost out, according to Noreen Nash.
Dean starred in the movie Giant with Taylor and Hudson, but he died before the film was released.
"Elizabeth and Rock took bets on who could get James Dean into bed first.
"I had an idea Rock would win but Elizabeth wasn't so sure. James was troubled but gorgeous," said Ms Nash, according to the Daily Express.
She reports that Ms Taylor lost her bet just days into the filming of Giant in 1955.
Dean was killed in a road accident on September 30th 1955 in a road accident.
The true nature of his sexuality has been endlessly argued over in the five decades since his death.
Some friends claim he only engaged in gay sex for "trade," others that he was bisexual.
Rock Hudson's death from AIDS in October 1985 brought the disease into the consciousness of many Americans for the first time.
His worldwide search for a cure drew international attention.
After his death his long-time lover Marc Christian successfully sued his estate, again calling attention to the homosexuality Mr Rock had hidden from most throughout his career.
Elizabeth Taylor eventually married eight times, twice to Richard Burton, and won two Academy Awards.