McCartney's daughter is also all for the collaboration, but McCartney fears the Radiohead frontman wouldn't be into it.
"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'," he said. Yorke is currently on tour in support of his other band, Atoms for Peace.
McCartney also said that working with Bob Dylan has been in the back of his mind for quite some time. For now, McCartney is busy preparing for the release of his upcoming album, New, which is due out on October 15th.