According to Sportitalia, the defender has accepted a contract proposal from Manchester City.
It’s believed to be worth €9m per season upfront, plus up to €3m in performance-related bonuses.
This would effectively double his current salary at the Stadio San Paolo.
There are multiple reports Manchester City will increase their offer to Napoli over the next few days to circa €70m plus bonuses.
President Aurelio De Laurentiis is prepared to lower his original €80m asking price to €75m including add-ons.
The first choice to replace Koulibaly is current Arsenal centre-back Sokratis Papastathopoulos.