But in one of the worst moves in Hollywood history, Monroe's management team advised her to reject the part which famously went to Audrey Hepburn.
It became the defining role of Hepburn's career which also made her a fashion icon.
The novelist Truman Capote wanted Monroe to play Holly Golightly in the 1960 film adaptation of his book Breakfast at Tiffany's.
She turned it down because it was considered that playing a call girl-like character would harm her image.
The script, that is now going up for sale, is accompanied by a scathing report by Monroe's manager Edward Parone, who described it as “empty” and “lacking warmth and importance.”
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He added the words: “I think not” when giving his opinion on whether Monroe should take the role.
The film was a huge hit and won two Oscars. Hepburn was nominated for an Academy Award for best actress.
The script, which is dated July 9, 1959 and comes with a shooting schedule for the film for November 1960, is tipped to tell for £7,000 at auction.
However, it could fare far better than its conservative estimate as Hepburn's own script for the film fetched a world record £632,000 when it went under the hammer in London last month.
The script comes from the estate of Monroe's acting coach, Lee Strasberg, to whom she left everything to following her death in 1962.
Monroe's management team advised her to reject the part which famously went to Audrey Hepburn
Martin Nolan, of US-based Julien's Auctions who are selling the script, said: "What is most interesting about this item is that it reveals Marilyn was offered the role but turned it down because her advisers told her not to take it.
"The script comes with a scathing letter from the head of Marilyn's production company which sets out why it was wrong for her.
"Marilyn was a keen reader and I imagine she would have poured over the script but she would listen to her acting coach Lee Strasberg and her management when making decisions.
"It would be fascinating to re-write history and wonder if she would have taken the role what it would have done to her career and Audrey Hepburn's career.
"There is a huge global interest in anything to do with Marilyn and we are hopeful this script will do much better than the estimate."
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A never-seen-before archive of intimate letters written by Audrey Hepburn has come to light. The archive is tipped to fetch £4,000 when it goes under the hammer
In the one page 'report' by Parone dated September 23, 1959, he doesn't hold back in his withering assessment of George Axelrod's screenplay.
Parone writes: "It is a curiously empty script. There is almost no drama at all, and it is not very funny.
"I found Holly unbelievable, more a literary stunt than a person.
"I can see Marilyn playing a part like Holly and even giving this present one all the elan it badly needs, but I don't feel she should play it.
"It lacks insight and warmth and reality and importance."
The auction takes place on November 17.