Chelsea and Manchester City are also reported to be keen on securing the Uruguayan's services to help improve their squads ahead of the new Premier League season.
But, speaking to 'El Partido de las 12', Cavani had nothing but praise for the La Liga giants when asked about a possible move.
Cavani said: "I am very calm. Real Madrid are a beautiful team, every player dreams of playing there when he is a child.
"Those are things that they are talking from behind, as it will soon be seen. But officially nobody has talked with me."
Cavani is currently with the Uruguay squad in Brazil which is taking part in the Confederations Cup and he says any talk about his future can wait until after the tournament.
Cavani added: "I am for now a Napoli player and I am focused on the Confederations Cup.
"What the clubs decide doesn't depend only on me, but also on other factors which will be talked about once the tournament is over."
Cavani hit 29 goals in 34 appearances for Napoli last season.