The Uruguayan international wants to hold talks with Napoli president Aurelio De Laurentiis in an attempt to persuade him to lower the club's asking price.
Cavani has been linked with Chelsea, Manchester City and Real Madrid, while reports today claim Manchester United are also considering a £50m bid.
But the Napoli forward fears his valuation is putting off suitors, and scuppering his chances of moving to a bigger club.
Speaking to Spanish newspaper Marca, Cavani said: "I don't think I'm worth €63m. I will have to talk to De Laurentiis about it. I owe a lot to Napoli and I want to leave through the front door if I move on.
"I am feeling very good at Napoli, but it all depends on the club. We will have to wait and see what options I have. What I want to do is sit down face-to-face with the club president and decide my future together."
Napoli have repeatedly insisted that Cavani will not be allowed to leave the club until his release clause is met.
Club president De Laurentiis revealed earlier this week that he expects the 26-year-old to make up his mind before July 20.
Speculation has been rife regarding his future for much of the summer, with reports claiming both Manchester City and Chelsea have had bids turned down for the forward.
But it is believed Napoli want a straight cash transfer for Cavani.