The Sun says Roberto Mancini is a long-term fan of the Uruguayan forward who shone against his team in the Champions League last season.
Cavani signed a new deal with the Serie A club at the start of the season but it is believed to include a £51million buy-out clause.
And his agent, Mino Raiola, said: “For now Cavani will stay but I wouldn’t be so sure about that once June arrives.
“You are intelligent enough on your own to understand where Cavani will play his football next season.”
Mancini is likely to be told he must move one his current quartet of strikers out if he wants to buy another one during the close season.