Presley's longtime confidante BYRON RAPHAEL, who was hired to wrangle beautiful one-night stands for the king of rock 'n' roll, reveals his boss met with Monroe on a film set at 20th Century Fox studios in Hollywood.
But, he tells men's magazine Playboy, the encounter never hit the headlines because Presley was keen to play down the fact the actress had turned down his advances.
However, Raphael insists Monroe was initially interested - until she spotted Elvis' entourage and quickly learned how dumb they were.
Raphael recalls the actress was particularly put off by Elvis' "dim-witted cousin" GENE SMITH and his pal CLIFF GLEAVES, "a hooligan".
Of the brief meeting, he says, "Monroe smiled in a way that said she liked how Elvis filled out his Oxford trousers, but then her face fell as she took in his companions.
"Monroe, forever insecure, had been searching for class in her choices of husband and lover and the sight of Elvis' barely civilised friends launched an unmistakable look of fear and disgust."
Smitten Presley continued to woo Monroe until she became one of the only women ever to turn down a date with the King - when she cried off with a headache excuse.
Raphael says, "It was one of the rare times Elvis was refused."