The 25-year-old has been a prolific marksman for the Partenopei, scoring nine goals in 16 Serie A starts this term.
However, his contract expires in June 2021 and Napoli want his future defined as soon as possible.
Napoli’s sporting director Cristiano Giuntoli spoke with Milik’s agent, David Pantak, by phone this week.
Giuntoli made it clear that there will be no more waiting and Napoli want an answer in 20 days.
The club’s position is that Poland international Milik will not be sold for anything less than €50m.
Napoli have been trying to renew Milik’s contract for six months and Giuntoli’s deadline is said to have ‘shaken’ him.
Juventus propose Cuadrado
Napoli are said to be seriously thinking about that idea, which would depend on the Colombian accepting the transfer.
Another issue could be Matteo Politano, who is on loan at Napoli from Inter, but with an obligation to buy him.
The arrival of Cuadrado could unsettle Politano, who is expecting more game time when Jose Callejon leaves Napoli this summer.
Tuttosport claims that Juventus are in pole position for Milik, although could face competition from Spain and England.