With the Serie A outfit having seen interest in their Uruguayan frontman mount steadily over recent years, they have moved to secure his future in Naples.
A €63million (£54.5m) buy-out clause has been inserted in his contract, pricing most clubs out of the market.
Napoli appreciate that their hand could be forced if their demands are met over the summer, but president Aurelio De Laurentiis is optimistic regarding the club's chances of retaining Cavani's services for the foreseeable future.
He told La Gazzetta dello Sport: "The clause of €63million? No-one has paid it.
"Last summer I refused €55m and Real Madrid didn't even get to 50.
"If someone meets it then there is nothing I can do, but I would do everything to convince the player to stay because it takes an agreement with him too.
"The last thing I am thinking about is depriving myself of Cavani. I like him as a player and as a man."
On the latest rumours regarding his future - with the likes of Real Madrid, Manchester City and Paris St Germain said to be leading the hunt for his signature - Cavani told Radio Marca: "I'm having a great time at Napoli.
"My future? The aim is to continue to grow, but right now I am only thinking about helping Napoli to realise their dreams."
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