The 25-year-old is expected to leave Liverpool this summer after failing to establish himself under new manager Arne Slot.
With just seven goals and five assists in his 45 games across all competitions, Nunez has been linked with several clubs in Europa and Saudi Arabia.
Now, according to transfer guru Fabrizio Romano on the "Here We Go" podcast, Napoli have entered the race to sign the Uruguayan.
Napoli are hoping to build upon an already impressive Serie A campaign, in which they sit at the top of the Serie A table with two games to go.