According to Tuttosport, the English club's owner, Sheikh Mansour bin Zayed Al Nahyan, is desperate to bring the Uruguay international to Eastlands this summer.
The Italian paper claims that City are ready to offer the 25-year-old forward a contract worth €4-5m per season.
Napoli's outspoken owner Aurelio De Laurentiis has resisted all previous opportunities to cash in on his Uruguayan star, but his resolve could be tested by a €50m bid from the Premier League leaders.
Cavani moved to the San Paolo from Palermo in 2010 for €16m. He has scored over 50 goals for Napoli in all competitions in just under 80 appearances.
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