The Bosnian forward, who is valued at £20m by the Blues, is wanted as a makeweight by the Italians.
City have so far bid £35m for Cavani and are also willing to throw Dzeko into the equation.
But the 27-year-old, who has two years remaining on his existing deal, is not keen on the Naples outfit and a move to Italy in general, unless it is to join his boyhood idols AC Milan.
The player would prefer to return to Germany and is hoping Borussia Dortmund will follow through on earlier interest.
City know they are in a rush and that Chelsea are rival bidders for Cavani's goalscoring prowess.