Manchester City are bidding to snap up Koulibaly, but have been holding talks with Napoli through an intermediary, rather than discussing with the Serie A side directly.
Napoli are determined to earn a big fee from the centre-back’s departure and have so far not received an offer from Manchester City good enough to tempt them.
However, according to Sky Italia, a new bid is expected to go in next week.
Manchester City are expected to offer a package worth €75m for Koulibaly, including add-ons.
If Napoli choose to cash in then they could focus on making signings, with the club looking to strengthen Gennaro Gattuso’s squad.
The club’s president Aurelio De Laurentiis is expected to have the final say, with Koulibaly not ready to go to war to force an exit from Napoli.
The powerful centre-back is happy and settled at Napoli, and is not willing to burn bridges to leave the club.