The Serie A club are flush with cash after agreeing the sale of Uruguay striker Edinson Cavani to Paris St Germain for a reported fee of 64 million euros (£55m) on Tuesday and are looking to strengthen their squad for their domestic and Champions League campaigns.
Asked in a Twitter chat with fans whether Napoli were negotiating to buy Higuain and Damiao, De Laurentiis said: "It's true."
"Raul Albiol is undergoing medical tests. We hope he passes," he added.
He also said that Napoli have €124.5m at their disposal for new players.
“If we add that €64.5m to the €60m that we had in our budget already then we get €124.5m that Napoli will invest with diligence and experience,” he noted.
Napoli last week agreed to sign versatile Spanish forward Jose Callejon from Real having already secured the services of Belgium winger Dries Mertens.
The pair have joined up with Spaniard Rafa Benitez, who was appointed Napoli coach at the end of May.
The former Liverpool, Chelsea and Inter Milan manager replaced Walter Mazzarri, who quit after the team finished second behind Juventus last season to qualify for Europe's elite club competition.
De Laurentiis added that Napoli’s new strip and club anthem will be unveiled on July 29 ahead of a friendly with Galatasaray.