The Chelsea and Real Madrid target has been connected with a summer move and was also linked to Manchester City before they decided not to meet his €63million (£54m) buyout clause.
That clause in Cavani's contract expires on 10th August, which has led to speculation he could wait until then to leave Napoli in order to secure a better deal for any future club.
But De Laurentiis thinks the Uruguay international, who is currently in Brazil at the Confederations Cup, will decide his future before he returns from a summer break on 20th July.
De Laurentiis told Radio Rai: "I don't think Cavani will leave on 10th August, when his buyout clause expires.
"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."