The actor had become an overnight success thanks to the film Midnight Cowboy and he was walking down London's King's Road when a fan told him Lennon was dining nearby - and he decided it was time for him to meet the singer.
He recalls, "I went to the door of the restaurant and I asked one of the maitre d's... 'I don't wanna bother John, but could you tell him Jon Voight, the actor..., is out here (and) would love to come in and say hello.'
"I was thinking, 'This will be fun...' And the maitre d' comes back and goes, 'Mr. Lennon doesn't really want to be bothered...'
"I just made my way back to my little apartment with my girlfriend... I never did meet John; I would have liked to."
Voight's Lennon tale features among Fab Four anecdotes from stars like Graham Nash, Peter Noone, George Martin, Justin Hayward, Art Garfunkel, actor Sir Ben Kingsley and Ray Manzarek in new movie Beatles Stories.