The 52-year-old musician revealed that he has recorded music with the legendary Beatles star and he hopes to use it on an upcoming album from Gorillaz, the virtual band he setup with comic book artist Jamie Hewlett.
Speaking on Dutch podcast 'Kink', Damon said: "I have a recording of Paul and myself that I could use for a Gorillaz track. It could easily fit on a Gorillaz album. It's a very simple, basic recording but I would never release it without talking to him first."
Damon went on to insist that the recording is not a full track but praised Paul, 78, as "one of the most special pop musicians".
He said: "[I don't want to say I have] a track with Paul, because I don't, but I could definitely work with him. He is one of the most special pop musicians ever."
Meanwhile, Gorillaz are also eyeing up another collaboration with a musical icon, after Jamie recently revealed Damon had a written a song for Dolly Parton.
Speaking to DIY, he said: "I suggested working with Dolly Parton imagining Damon would throw it back in my face and he turned around and was like, 'Are you serious? I f****** love Dolly Parton'. So we need to find a way of getting in touch with Dolly. Damon's already written the track, I think! We had this conversation three weeks ago when he was in Paris, and I spoke to him the other day and he said, 'I've written that one'."