The striker, who has notched 102 goals in 124 matches during his time in Naples, looks increasingly likely to leave the Serie A club
The 26-year-old recently admitted the chance to work with City manager-to-be Manuel Pellegrini would be "a pleasure" following news a player-plus-cash deal involving Edin Dzeko had stalled.
Chelsea have also registered their interest with a player-plus-cash bid of their own involving Fernando Torres, but Berta Gomez claims just City and the Liga giants are currently in the running for her son's signature.
| TRANSFER TALK
|4/1||Edinson Cavani is 4/1 with BetVictor to join Manchester City this summer
"The Napoli president, Aurelio De Laurentiis, has spoken to Chelsea but there’s nothing concrete. In 15 or 20 days we'll know his destination.
"In any case, I assure you Edinson loves Naples, and if he goes he will never forget the love and affection of the people."
City are understood to have agreed a £150,000-a-week deal in principle with Cavani - who has attracted admiring glances from a number of top clubs in Europe - with new boss Rafael Benitez green-lighting a potential part-exchange with Dzeko.
However, De Laurentiis has already made it clear the club will only let Cavani go if his €63 million [£53.5m] release clause is triggered.
The Uruguyuan, who is currently preparing for his country's Confederations Cup campaign, has enjoyed three prolific seasons with Napoli - notching 102 goals in 124 matches for the club in all competitions