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.
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"I don't think Cavani will leave on August 10, 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 20 we will probably know everything about his future."
Cavani joined Napoli from Palermo in 2010 for £10 million, and has played 52 games for his country, scoring 14 goals.