The 26-year-old is one possible target for the Spanish side as they search for a replacement for Gonzalo Higuain.
Chelsea and Manchester City are also believed to be tracking the Uruguayan, who scored 36 goals in all competitions last season.
"Cavani's intention is to play for Madrid," Luis Cavani told Futboleros. "He is excited about it and is very willing to see it through.
"He has told the family in private that he wants to join Real Madrid but if he declares it publicly it will annoy Napoli."
He added that representatives from Madrid had already held talks with the player but is concerned that Napoli's valuation of his son may prove a stumbling block.
"There has been contact with Real Madrid's lawyers and now we are waiting for the two clubs to meet," he said.
"I hope it happens and that talks take place as soon as possible. Who wouldn't want to play for Real Madrid?
"It's not just up to Edi. They are talking about 65 million euros and Napoli won't negotiate for any less."