The Uruguayan, who has also attracted attention from Chelsea recently, is said to the Sky Blues’ top transfer target, as manager Roberto Mancini plots an overhaul of his squad this summer.
Despite some off-field issues, the 26-year-old has still managed to net a staggering 28 goals in all competitions this term, leading to speculation that he could make a big move at the end of the season.
Napoli president Aurelio De Laurentiis has hinted that the club are willing to sell Cavani, but they are believed to be keen to have a replacement lined up.
City may use Dzeko as a potential makeweight in a move, with the Bosnian forward rumoured to be one of the players Mancini is willing to let go of.
Even though he has endured an underwhelming spell in the England, the former Wolfsburg man is still thought of highly throughout Europe, and his inclusion could tempt the Serie A.
Cavani is believed to have a release clause in excess of £50m, so City would still have to include a sizable sum of cash to force through a deal.