It would appear Real and City are leading the race for the Uruguay international as they aim to activate his reported £53million buyout clause.
"Edi is dealing with Real Madrid and City," said Cavani's mother, Berta Gomez, in a radio interview in Montevideo, Uruguay.
She added: "In two or three weeks, we will know their fate and be able to say more.
"In any case, I assure you Edinson loves Naples and, if he goes, he will never forget the love and affection of the people."