Cavani has been heavily linked to Chelsea, Real Madrid, and previously Manchester City, before their initial proposed player-plus-cash deal involving Edin Dzeko stalled, as Goal revealed.
The Uruguay international has scored over 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 10th August, 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 20th July we will probably know everything about his future."
Cavani joined Napoli from Palermo in 2010 for €12 million, and has played 52 games for his country, scoring 14 goals.