The late musician was with his secretary May Pang, when the pair were at his New York apartment on August 23 1974.
The Beatle’s sighting was recounted in the book Ms Pang later went on to write entitled Loving John.
She wrote: “The large, circular object was coming towards us.
“It was shaped like a flattened cone and on top was a large, brilliant red light. When it came a little closer, we could make out a row or circle of white lights that ran around the entire rim of the craft.”
Lennon was separated from his lover Yoko Ono at the time.
He later referred to the sighting on the cover of his solo album Walls And Bridges, released the same year, saying that he saw a UFO.
In Ms Pang’s book, she continued: “We had just ordered up some pizzas and since it was such a warm evening, we decided to step out on the terrace.
“There were no windows directly facing us from across the street, so John just stepped outside with nothing on, in order to catch a cool breeze that was coming in right off the East River.
“I remember I was just inside the bedroom getting dressed when John started shouting for me to come out on the terrace.”
She said she yelled back she would be right there, but Lennon screamed for her to join him that instant.
She said: “As I walked out onto the terrace, my eye caught this large, circular object.”
She said it was not pulsating, like one on the many aircraft they had seen landing at Newark Airport.
She described the lights around the rim.
She said: “They were flashing on and off. There were so many of these lights that it was dazzling to the mind. It was, I estimate, about the size of a Lear jet and it was so close that if we had something to throw at it, we probably would have hit it quite easily.”
She claimed the object just eerily passed by.
She added: “We often had helicopters flying above us but this was as silent as the night and about seventeen storeys above street level.”
She told how the object flew off but returned later.
Lennon had set up a telescope by this point so they were able to view it in better detail.
She recalled: “The light was so brilliant coming from the craft that no additional details could be seen. We did take a couple of pictures but they turned out overexposed.”
She said they also rang a local newspaper to report the sighting and were told at least seven other people had seen the UFO too.
She said: “We even called the police, that’s how excited we were, and they told us to keep calm, that others had seen it too.
“During what was left of the evening, John kept saying, ‘I can’t believe it… I can’t believe it… I’ve seen a flying saucer!'”
