The Jamaican sprinter, who won gold in the 100m, 200m and 4x100m relay at London 2012, believes that the 33-year-old centre-back has enough contacts to launch his music venture.
"If we do this together we could take it to a new level," Bolt told The Sun.
"Not since Bob Marley have we had a musician famous all over the world and believe me, it's nothing to do with lack of talent.
"Our musicians are as good as our sprinters. It just needs people with global fame like me and Rio to move things."
This is not the first time that the 26-year-old has been linked with the former Premier League champions. The world-record holder recently claimed that he is good enough to play in Sir Alex Ferguson's side.