However, De Laurentiis feels that Cavani will show his true colours by staying with the Serie A runners-up.
"I believe he is a real man and will therefore remain at Napoli," De Laurentiis told Radio Rai.
"If he does decide to go, it will in any case be after the Confederations Cup. I trust in the man, then if he doesn't want to it'll be a joke on me.
"We will know everything by July 20. If not, I'll smack him!"
Cavani was the top scorer in Italy last season, netting 29 goals in Serie A.