Sir Paul McCartney wants to make a record with Thom Yorke. The former Beatle revealed that he's keen to record some music with the Radiohead frontman – but is nervous Yorke will turn him down.

"[My daughter] keeps saying to me, 'Ring Thom and just go into the studio and just see what you come out with,'" McCartney told NME in a new interview. "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'."

Although Stella McCartney is "very keen" for her dad to move forward with the Macca/Yorke team-up, McCartney senior seems just as determined to work with an older, less newfangled peer: Bob Dylan. The idea has been in the air for ages: McCartney complained in 2009 that Dylan seemed reluctant to "[get] in touch". Now, four years later, McCartney admitted that the notion is "still … at the back of my mind". "I would like to do it," he said.

Since the Beatles split in 1970, McCartney has never been shy about working with other stars. He has recorded music with everyone from Michael Jackson to Johnny Cash to mash-up master Freelance Hellraiser; more recently, he has teamed up with both the Bloody Beetroots and the surviving members of Nirvana.

McCartney also explained that his forthcoming solo LP, New, was a kind of experiment. Whereas 2012's Kisses on the Bottom was a jazzy throwback album, the new one was recorded with several of Britain's most celebrated contemporary producers: Mark Ronson, Paul Epworth and Ethan Johns.

• New will be released on 14 October.