The Uruguay international is unhappy with the Serie A side's excessive demands and is keen to open talks with club president Aurelio De Laurentiis.
Napoli president Aurelio De Laurentiis stressed last week that the Serie A outfit will only allow the 26-year-old to leave if an interested club meets his 63m euro buyout clause, but Cavani feels his price tag does not represent his actual value and he hopes to convince the club to lower its demands.
"I don't think I'm worth 63m euros. 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," Cavani told Marca. "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.
"Real are one of the best clubs in the world, but there is no deal yet. When you're a kid, you dream about playing at a team like Madrid or Barcelona, but right now I'm at Napoli and I'm very proud to be there. If I leave one day, I'll be ready to move to a bigger club. We'll see."
The Uruguay international already demanded showdown talks with De Laurentiis on Monday following the Napoli president's comments that he expects the striker to make up his mind before July 20.
Cavani's current contract with Napoli runs until the summer of 2017.