The much-coveted striker has a buy-out clause of £60 million but it is now being claimed that Partenopei president Aurelio De Laurentiis would be willing to accept a smaller fee
The Uruguay international's future has been the subject of much debate for two years and Partenopei president Aurelio De Laurentiis admitted earlier in March that he would be willing to part company with his most prized asset should any club meet the €70 million (£60m) asking price.
As revealed by Goal.com, Manchester City and Chelsea both also maintain interest in the Uruguayan as an alternative to Atletico Madrid star Falcao.
However, Cavani's father believes that Napoli will actually allow the striker to leave the San Paolo for less than the figure stated in the player's buy-out clause.
"Napoli have refused offers from a lot of teams, but I believe that if an offer of €60m [£50.6m] arrives, he will be sold," Cavani senior told Marca TV.
"I believe that today there is a 50% chance of signing for Real Madrid but the negotiations with Napoli will be very complicated."
Cavani has established himself as one of the most lethal forwards in world football since joining Napoli from Palermo in 2010.