Cavani has been heavily linked to Chelsea, Real Madrid, and previously Manchester City, before the club's proposed player-plus-cash deal involving Edin Dzeko stalled.
The Uruguay international has scored more than 100 goals for Napoli in his three seasons at the club, and De Laurentiis is confident Cavani will not leave after the clause in his contract runs out.
"I don't think Cavani will leave on August 10th, when his buyout clause expires," De Laurentiis told Radio Rai. "I'm confident in him, because I consider him a real man. He won't make me a joke of me.
"Should Cavani want to leave, he will decide it after a long period of reflection. But by July 20th we will probably know everything about his future."
Cavani joined Napoli from Palermo in 2010 for 12 million euros, andhe has played 52 games for his country, scoring 14 goals.