Aurelio De Laurentiis, owner of the Naples club, revealed last week that Cavani’s latest contract has a €63million release clause.
However, despite reports suggesting Russian side Zenit St Petersburg matching the required amount, Manchester City confirming interest in the striker, and rumoured interest from the likes of Real Madrid and Chelsea, the 25-year-old quashed talk of a departure.
"I hope to stay here for a long time,” he told TG1.
“I am enjoying this moment and everything that surrounds football in this city, such as the fans, who give us an extra boost.
"Naples has given me so much and that is why I am so happy here. The warmth and affection of the fans have given me extra confidence. I have a great deal of love for them and for this city.
“My children are Neapolitan, as they are indelibly linked to this city, because they give me everything and I try to give something in return."
The Uruguay international also took the time to praise the work of coach Water Mazzari and his team-mates.
"Some players like to go out partying but I like the quiet life," Cavani said.
"My team-mates are my family, I spend so much time with them and am very close to the players and those who work for Napoli. I focus on winning and on getting important results with Napoli.
"Walter Mazzarri is right when he says much of my success comes from the team. A striker scores goals, but the goalkeepers saves them, the defenders close chances down and all the credit is shared out.
“A lot of the credit also goes to the coach, who prepares us for the games brilliantly."
However, the links away from Stadio San Paolo are likely to continue, particularly after Cavani’s father appeared on Marca TV on Thursday night and claimed a move to Real Madrid would be “ideal for my son”.