The 26-year-old has a £54m release clause in his contract which expires on 10 August, but De Laurentiis is optimistic Cavani will have decided his future by the deadline.
“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 20 July we will probably know everything about his future.”
On Saturday, the Napoli striker expressed his interest in a potential move to Chelsea or Real Madrid – who are the only side to have lodged a bid.
“In this moment I don’t know [anything] about my future,” Cavani told Ovacion.
“It will be difficult to say no if there will be offers of Chelsea or Real Madrid.
“I will do my 100 per cent only for the club that will show strong interest in my person. In this moment there isn’t nothing concrete.”