Steve - who died in 1980 aged 50 - asked Twiggy to dance, but she was with her boyfriend and opted not to take to the floor.
Speaking to Jessie Ware on her 'Table Manners' podcast, she said: ''I was flying around the world and being given parties where Clint Eastwood was there and Barbra Streisand.
''It was mad... Sonny and Cher threw me a party.
''One of the biggest film stars was Steve McQueen - he was gorgeous.
''I was 17 and I was with my boyfriend and Steve McQueen turned up on his motorbike.
''We got introduced and he asked me to dance - and I said no.''
But Twiggy - who is married to Leigh Lawson and was previously wed to Michael Witney, who died in 1983 - insisted it's not a moment she looks back on with regret.
Asked by Jessie if it's the ''biggest regret'' of her life, she laughed and replied: ''Probably not.''
Twiggy - whose real name is Dame Lesley Lawson - was discovered at the age of 16 and was known for her iconic cropped haircut, big eyes and huge eyelashes, and the fashion legend recently admitted she would take almost two hours to practise her make-up.
She said: ''It used to take me an hour and a half to do, I had three pairs of false eyelashes on the top. I'm amazed I could open my eyes. Then I used to paint the lines underneath. So in 1966, when I was plucked from anonymity into the madness it became, that was my look.''
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