The Uruguayan forward has regularly been linked with a move to a bigger club, and refused to rule out a transfer earlier this month.
But De Laurentiis refuses to accept that the 25-year-old is set to leave Naples in search of another challenge.
“Cavani is a great guy and he is staying here, just like all the other players who want to remain at Napoli,” De Laurentiis told Il Corriere dello Sport.
De Laurentiis admitted, however, that Ezequiel Lavezzi has a buy-out clause in his contract, and conceded that the Argentine could be ready to move on.
“He (Lavezzi) wanted to have that clause inserted when he signed, so there’s a big chance it will be used at some point. We will just have to wait and see whether there are clubs ready to match his clause,” he said.
“Lavezzi is in my heart, but if he wants to leave, we will have to let him go if a team meets his buy-out clause.”