The Uruguay international, who is also a target for Manchester City, is on the radar of the west London club, with the owner also confirming an approach for Andre Villas-Boas.
The Uruguay international is also a target for Manchester City after notching 102 goals in 124 matches for the club in all competitions over three seasons.
Jose Mourinho was announced as Chelsea's new manager on Monday, signing a four-year deal, and looks close to completing a move for Schalke midfielder Andre Schurrle, but De Laurentiis has now claimed the Portuguese is after further attacking talents.
The Italian told Radio Marte: "Chelsea want Cavani. 'Blues' will call me in the next hours about it..."
De Laurentiis went on to say that if Cavani is sold, the club will reinvest the money from the move.
"If Edinson stays in Napoli I will be happy," he said. "If he goes, we'll replace him using the 63 million euros from his sale."
De Laurentiis also confirmed that Napoli made an approach for Andre Villas-Boas before appointing Rafael Benitez.
"I contacted Villas-Boas, but he had to go in the USA on tour, so I spoke with Rafa Benitez and he convinced me to choose him immediately," the chairman said.