The 26-year-old is in high demand, with clubs from across Europe keen to secure his services.
Premier League sides Chelsea and Manchester City are thought to be interested but Luis Cavani insisted that his son's preferred destination is the Bernabeu.
"Cavani's intention is to play for Madrid," he 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.
"There has been contact with Real Madrid's lawyers and now we are waiting for the clubs to meet. I hope it happens and that talks take place as soon as possible. Who wouldn't want to play for Real Madrid?"
The asking price could yet prove a stumbling block in proceedings, however, with Luis Cavani suggesting that Serie A outfit Napoli want 65 million euros for their star man.
"It's not just up to Edi," he added. "They are talking about 65 million euros and Napoli won't negotiate for any less."
It is the second time this week that a member of Cavani's family has commented on his future, following an interview his mother gave to a Uruguayan radio station in which she stated that he was in talks with Real and Manchester City.