The actor - who has portrayed a number of British icons on the big screen, including Tony Blair, David Frost and Brian Clough - said that although it is his desire to depict the late music icon, he is convinced that he would instead be cast as Lennon's bandmate Sir Paul McCartney.
He explained to Now: "I'd want to play Lennon, but I probably would be cast as McCartney!"
Sheen also revealed that he was too starstruck to strike up a proper conversation with McCartney when they met on a plane recently.
He added: "I met Paul McCartney on a flight not long ago. I was sitting there going, 'I can't go over there'. And then he came over to me. He said, 'You're famous, aren't you? I've seen you on the TV'. And I thought, 'Yeah, I've seen you on the TV a few times as well!'"