The Beatles icon admits his fashion designer daughter Stella is keen for the pair to hook up in the studio, but the Yesterday hitmaker is worried Yorke won't have time to fit him into his busy schedule.
He tells Britain's NME magazine, "My daughter Stella is very keen (for a Thom Yorke collaboration). She's got a project, she keeps saying to me, 'Ring Thom and just go into the studio and just see what you come out with.'
"I'm a bit sort of paranoid to just ring him up. 'Hey Thom, it's Paul here. What do you fancy, what are you doing? Do you fancy writing something?' Just in case he says, 'Er, actually I'm busy'."
However, there's one dream duet partner MCCartney is eager to turn into a reality: "There were big rumours a couple of years ago about me and Bob Dylan writing together (sic), and I've still got that at the back of my mind. I would like to do it."