The Premier League side have been negotiating with Napoli after their initial bid of €63m plus bonuses was rejected.
City are now willing to meet Napoli’s demands of €70m plus another €5-6m in bonuses.
In addition to that, City have agreed personal terms with the 29-year-old defender, another step towards securing him.
— Alfredo Pedullà (@AlfredoPedulla) August 18, 2020
Napoli had originally wanted €80m plus bonuses but decided to reduce their asking price to €70m plus bonuses.
Now they are waiting for City to make a new official offer and then the Italian club will most likely accept.
Senegalese defender Koulibaly has been a key member of the Napoli side since arriving from Genk in 2014.
He has made a total of 246 appearances for the Azzurri, scoring 10 goals during his time in Naples.