The British rapper is a huge admirer of the eclectic musician - who as well as fronting Blur also masterminded animated band Gorillaz and started The Good, The Bad and The Queen with former The Clash bassist Paul Simonon - and would love to record a track with him.
He said: "I wouldn't mind do something with Damon, he's a great artist."
Although Just Jack, 34, is a fan of 40-year-old Damon now, he didn't like Blur at the height of their Britpop fame in the mid-90s.
He added: "At the time, I hated Blur and Oasis and I'd be honest and I'd tell Damon I wasn't a fan."
If Just Jack does get his wish, it was recently revealed Damon always has a "plethora" of new songs waiting to be recorded.
The Blur star's manager Chris Morrison said: "He's got a plethora of tracks at the moment. Whether they all make the light of day or get refined and come down to a normal amount you get on a record of 10 to 15 tracks, I can't tell at this point in time."