Both Nunez, 25 and Chiesa, 27, are expected to leave Liverpool this summer after they have not had a real impact under manager Arne Slot.
According to journalist Gerardo Fasano, the two have agreed to join Antonio Conte while they want to build on their recent Scudetto victory.
Fasano has also suggested that Liverpool could use the two in a movement for striker Victor Osimhen, although the Nigerian still has to agree with such a movement.
He said to Areanapoli: “Chiesa and Nunez have already said yes to Napoli, this is the news I can give you and it refers to the very last hours of the transfer market. What is missing to close the deal?
“Victor Osimhen's Yes has not yet been given. Moreover, both Napoli and Liverpool are working on defining the details regarding the costs of the players' registration cards.”