Napoli president claim Chelsea want Cavani
"Chelsea are interested in Cavani and they will call me soon," De Laurentiis told Napoli's official radio station Radio Marte from Los Angeles On Friday.
"I'm very happy that his brother has said that he will stay, but if he did decide to go to Chelsea we would take time out to think and replace him with people worthy of replacing him."
Uruguayan Cavani was top scorer in Serie A last term, netting 29 goals in 34 appearances as they challenged for the title and finished second behind Juventus.
He is also Napoli's third highest goal-scorer with 104 goals in three seasons, 11 behind Diego Maradona, who scored 115 in seven seasons.
Film mogul De Laurentiis also revealed in the interview that he has offered 40 million euros for AS Roma pair Erik Lamela and Marquinhos.
"I contacted Unicredit [Italian bank which part-owns Roma] directly for Lamela and Marquinhos. I offered them 40 million," he said.
"They wanted to sell me the services of [Pablo] Osvaldo at all costs, but, seeing that for now we have Edinson Cavani we don't need him.
"This all happened before Benitez signed and I thought I'd done good business for two young players. Then however I began to wonder if they were really worth that amount of money."
Napoli are looking to strengthen their squad for next season, hoping to build on an impressive campaign that saw them qualify for the Champions League.
Former Chelsea boss Rafael Benitez has replaced Walter Mazzarri as manager after the latter moved to Inter Milan and will need a bigger squad if they want to compete domestically and in Europe.