The 26-year-old is one of a number of attacking options Madrid are weighing up with Gonzalo Higuain seemingly set to move on, while Chelsea and Manchester City are also believed to be keen to secure his services.
"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.
"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?
However, Luis Cavani warned that any deal for his son could prove difficult to negotiate given the reported 65 million euro (£55m) fee Napoli are demanding for the 29-goal top-scorer in Serie A last term.
"It's not just up to Edi," he said.
"They are talking about 65 million euros and Napoli won't negotiate for any less."
- Real Madrid