Rossi has recently been linked with moves to the likes of Barcelona and Juventus, but The People reports that City have now joined the race.
City are reportedly ready to make a £18million bid for the striker, but Villarreal are looking for around £30million for the Italian.
City are ready to include first-team fringe players into the deal in a bid to sign the striker.
Rossi is reportedly keen on a move to Barcelona.