Former fashion model Pat Cleveland is opening up about her fleeting romance with the late heavyweight boxing champion Muhammad Ali in Miami in 1966.

“I picture us running and laughing on the beach, he and I alone, in the morning and then having to go back to the hotel to have breakfast together with all of his secretaries and assistants,” Cleveland, author of Walking with the Muses: A Memoir, tells PEOPLE. “He was just a lovely human being he just wanted to get away from the fame for a minute and I was that outlet for him.”

She adds, “I got to be a part of his private moments of happiness, and I’ll always remember that.”

The pair met at a Florida fashion fair, where she was walking in a runway show.

“I was 16 and he must have been 22 or 23 and he wasn’t Muhammad Ali, he was just this young boxer, he was Cassius,” she says. “We were together in the elevator with his people and my mom. He took a liking to me. He was trying to woo me!”

They inseparable for the next week – spending time on South beach, riding around town in Ali’s convertible and reading the Miami Herald newspaper to each other.

“He said he liked having me around because I was innocent,” says Cleveland. “I just thought he was a cute boy who was funny and sweet. We were buddies at first sight!”

Cleveland recalls one particular sunny Miami morning when Ali chased her around the beach – and hinted at marriage.

“I was coming out of the water when he came running up behind me and grabbed my towel off the ground, threw it around me and picked me up,” she says. “He goes ‘You can’t be running around in that little white lace bikini if you’re going to be my wife!’ ”

“I thought, ‘Oh my gosh, is he insane?’ He was such a jokester!”

Of reading the paper after their beach strolls, she adds, “He was on the front pages of all of the papers! He was like a giant soft teddy bear [to me] but he had to be tough to the rest of the world.”

The former model says Ali liked to “show off” his toughness to her.

“He said to me ‘Look, my hands are a weapon, do you want to see what it looks like if you stand in front of me and I throw a punch at you?’ ” says Cleveland. “He balled up his fists and came right towards my face and stopped right at my nose and his fist was as big as my face. It looked like a train engine coming at me! But he smiled and said ‘Don’t worry I would never hit you because these are lethal weapons.’ ”

The beloved boxing champ would drive around Miami’s low-income neighborhoods with the model – slowly cruising down streets in his Cadillac convertible as fans rushed to his car. Ali was “trying to impress” her, according to Cleveland.

“He would say ‘Watch this! This is where the people really love me!’ and then stand up on the back seat as we drove through neighborhoods,” says Cleveland. “He started pounding his chest and he kept saying ‘I’m the greatest, you bet on me – you bet on the best!’ ”

When the fashion fair ended, Cleveland and Ali’s short-lived relationship faded.

“He called me a few times over the years, wherever I was, he kept trying to pursue me!” says Cleveland. “In the end, his career took over and mine did as too, so we didn’t have time for each other.”

Rest in peace my dear friend. …it was nice knowing you when you were very young, we had wonderful moments together….

— Pat Cleveland (@iampatcleveland) June 4, 2016

Cleveland would see Ali only one more time – and she says his eyes “lit up” when he recognized her.

“He was at a Valentino show, at the end of the runway,” says Cleveland. “I looked at him and he looked at me and it was lik,e ‘Hey remember we know each other? We had a moment on the beach years ago.’ ”

Pat Cleveland’s book Walking with the Muses: A Memoir will be released on June 14. She dedicates a chapter to her time with Muhammad Ali.