Benitez has signed a two-year deal to take over at the Serie A club, following his stint as interim manager at Chelsea.
The Italian media report that Benitez is keen on bringing Reina in to replace Napoli’s current first choice goalkeeper Morgan De Sanctis.
Reina has been linked with a move away from Anfield this summer, more heavily with Barcelona.
But last week the Spanish international said there was no truth in speculation linking him with a move to the Nou Camp.
“I’m happy there [Liverpool], and my wife and my children. [I] do not know if my agent knows something, but I did not.”
Benitez, meanwhile, has also been linked with moves to sign Daniel Agger, Martin Skrtel and Lucas since his arrival at the Partenopei.