The Uruguayan has remained with the Serie A club despite attracting interest from some of Europe's top clubs, said to include Real Madrid, Manchester City and Paris St Germain.
Juventus were also reported to be on the cusp of offering the 25-year-old the chance to play Champions League football early this season, but instead he signed a new, five-year contract.
However De Laurentiis seems open to the prospect of losing his star player in the next transfer window if Cavani instigates a move.
"I have an extraordinary relationship with Cavani," De Laurentiis told Italian journalists.
"He has a five-year contract with us and we will evaluate what to do in the summer.
"If he were to convince me that his story with Napoli is over we'll talk, otherwise he will remain here."
De Laurentiis was less clear-cut about the future of head coach Walter Mazzarri, whose current contract expires at the end of the season.
The highly-rated Mazzarri, who has been at the Stadio San Paolo since 2009, has guided Napoli into second place in Serie A as they chase their first Scudetto since 1990.
"Mazzarri? His contract expires at the end of this season. He still has my esteem and I see no reason to change," De Laurentiis declared.
"We'll see if he still wants to stay, we will decide together."