The 'Come Fly With Me' crooner is believed to have asked the actress - who died of a drugs overdose, aged 36, in 1962 - for her hand in marriage in 1961, a year before her death, but she reportedly turned him down to get back together with her estranged husband Joe DiMaggio.
Sinatra's closest aide Jilly Rizzo told 'Sinatra: The Chairman' author James Kaplan: ''Yeah, Frank wanted to marry the broad. He asked her and she said no.''
Sinatra's feelings were so strong for the iconic Hollywood star that the book reveals DiMaggio and him became rivals and, as a result, he was not allowed to attend her funeral.
Talent agent Milt Ebbins added: '''There was no doubt that Frank was in love with Marilyn.''
A year later, in 1962, Kaplan wrote how Monroe accompanied Sinatra to his resort in Cal Neva, Lake Tahoe, to try and protect her from her downward spiral.
However a week later she took her own life.
The 'New York New York' singer and 'Some Like It Hot' actress first met in 1954, while Sinatra was still with his second wife Ava Gardner but after their divorce in 1957, the couple started courting for several months.
'Sinatra: The Chairman' is released on October 27.
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