"I said to him that he could stay for one more year or five more years," De Laurentiis told Naples radio station Radio Kiss-Kiss.
"If he stayed, I would be the happiest man in the world. Otherwise we will bring in a coach who is just as good."
It has been widely expected that Benitez would leave in the summer and he has been linked with leading European clubs such as Paris Saint-Germain and Manchester City.
Benitez joined Napoli in 2013 but his family is still based in the north-west of England, where he enjoyed a six-year spell in charge of Liverpool before leaving in 2010.
However, De Laurentiis said that Benitez's family "could move to Rome, where there are plenty of English schools. That would be perfect."
The Spaniard won the Italian Cup and led Napoli to third place in Serie A last season in his first campaign in charge at the San Paolo.
This season they have already won the Italian Super Cup, while they lie fourth in Serie A, two points adrift of the Champions League places, and have a Europa League semi-final to come next month against Dnipro of Ukraine.