The Beatles legend insists he has not yet been approached to sing at the London Games next summer but is willing to be involved if he is asked.
Asked by Absolute Radio Hometime DJ Geoff Lloyd if he has been approached to take part, he said: "I've no idea about that. Have they asked me? No, well I met a man who knew a man.
"They don't ask me to do everything. I haven't heard anything about that just yet.
"I'm not looking coy, but, you know, I'm working on it.
"Well, you know, its Olympic, very good running, very good jumping, very good swimming and all that. That's the basis, you know, and if they're interested in that I could think of doing it."
Paul received a knighthood in 1997 for services to music and can't understand why his former bandmate Ringo Starr ' the only other remaining surviving member of the group ' has not received a similar honour from Queen Elizabeth, and jokingly claimed he will ask the British monarch why his friend has been snubbed.
He said: "Don't look at me. I do know the queen, I do know her, but last time I went by she was out.
"The flag wasn't flying otherwise I would have popped in and said 'Look, love, Sir Richard Starkey'.
"It's got a ring to it. And he's got lots of rings. You see, well, I don't know, I'll try and pop in because I do think it's about time."