Both Nunez, 25, and Chiesa, 27, are expected to leave Liverpool this summer after failing to make any real impact under manager Arne Slot.
According to journalist Gerardo Fasano, the two have both agreed to join Antonio Conte’s side as they seek to build upon their recent Scudetto win.
Fasano has also suggested that Liverpool could use the two in a move for striker Victor Osimhen, although the Nigerian is yet to agree to such a move.
He told told 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 conclude the deal?
“Victor Osimhen's yes has not yet been given. Furthermore, both Napoli and Liverpool are working on defining the details regarding the costs of the players' registration cards."