The West Side Story icon - who played Anita in the original 1961 adaptation of the legendary musical - received a call the next day from Elvis’ manager, Colonel Tom Parker.
Doing an impression of the Colonel, she remembered him saying: “Turns out Elvis saw you with the commissary of the 20th Century Fox.
“He liked what he saw and he would like very much to meet you. Would you like to meet him?”
Speaking as herself, she added: “I saw the underwear and I said yes.”
Moreno - who first met Brando when she was 22 on the set of Désirée - previously described Elvis as “sweet but boring”.
Recalling the moment Brando found out about her romance with the Suspicious Minds singer, she told The View: “He started to throw chairs. He was so angry. It was wonderful. And I just sat there as he threw chairs and carried on.”
And she previously described the late actor as the “lust of her life”.
She told People back in 2017: “Why that picture of Marlon Brando [in my bedroom]? Because he was a big love of mine in my life.
“This one, it almost seems like a vignette out of a movie, so that’s why it’s there. He was the lust of my life and that over there [with her husband] is the love of my life.”