The 26-year-old Uruguay international had already been linked with a move to Manchester City before his mother claimed he had held productive talks with both City and Spanish giants Real Madrid.
Comments from his father then suggested Cavani had agreed to join Real, with the capital club apparently haggling over the striker's 63million euro (£54million) release clause.
But Cavani, who scored 29 league goals for Napoli last season, has called time on what he considers harmful interfering from his parents.
Quoted in La Repubblica, he told reporters: "My father has talked about Real? I want to point out that these words are not coming from me.
"I've asked my parents a thousand times not to say any more. They can only hurt me.
"I belong to Napoli as it stands and that depends on the club. If another option presents itself, we will evaluate it."
Napoli president Aurelio De Laurentiis has reportedly asked his club's talisman to make a final decision on his future by July 20, following his return from Confederations Cup duty with Uruguay.
And when asked if Real Madrid - now managed by former Chelsea and Paris St Germain boss Carlo Ancelotti - would be his preferred destination, Cavani remained cagey.
He added: "I will make myself clear on this point too - I've always said they're one of the best clubs in the world.
"We've all dreamed of playing for them, as we have with Barcelona, but now I'm at Napoli and very proud of the fact.
"If I leave the blue shirt behind one day, I will only do so to join a big club. Obviously there would be some fans who would understand and others who wouldn't.
"But I don't want to slip out of a back door, I want to walk out of the front door, on the day that finally happens."