Milik has entered the final year of his contract at Napoli and is keen to move on, but has seen potential switches to Juventus and Roma fail to take off.
He could move to the Premier League and has been linked with a host of clubs in England, including Tottenham, Everton, Manchester United, Fulham and Newcastle United.
Napoli face losing Milik without a fee if he sees out the final year of his deal in Italy and Guintoli is optimistic that a solution can be found.
The sporting director, asked about Milik, said on Sky Italia: “I am optimistic that we can find an important solution for both him and for us.”
Napoli could yet agree to loan out Milik with an obligation to buy, something which would need to see the Poland striker extend his contract at the club.
Intermediaries are at work on a move for Milik away from Napoli, but the clock is ticking on the transfer window.
Milik is just seven appearances shy of hitting the 100 appearances mark in Serie A and it is far from clear whether he will be able to hit the milestone.
