The 26-year-old is considered excess against the requirements in Liverpool after he had not settled under Arne Slot.
Nunez scored only seven goals and gave five assists in his 47 games in all games when Liverpool lifted the Premier League title.
Despite his lack of form, Serie A is strongly connected to Napoli with a movement for the Uruguayan, where Antonio Conte pushed to get a deal over the line.
Gianluca di Marzio has now reported that they have submitted a € 50 million plus € 5 million in add-ons for rush hour.
Napoli is also working on the signing of Lorenzo Lucca van Udinese, who could join them next to Nunez instead of instead.