The People says City have made a £45million bid for Cavani. The bid was made by City's sporting director Txiki Begiristain at Christmas.
Cavani himself would love a crack at the Premier League - and is convinced he would be as big a hit as his compatriot Luis Suarez.
"I know that there has been interest from Premier League teams," he said. "I know I would be a success in the Premier League - and it is an exciting prospect."