Koulibaly has been linked with a move to England for the last two years.
Manchester United were the early favourites to sign him, before Liverpool and City joined the race
But according to Italian journalist Alfredo Pedulla, it is City who will sign the Senegal international.
Chelsea director Marina Granovskaia has been in constant contact with his agent over a possible switch.
But it looks as though Koulibaly will instead choose Pep Guardiola at City.
Reports earlier this week suggested the Etihad side were ready to splash out £63million for Koulibaly.
The Premier League runners-up signed Nathan Ake from Bournemouth for £41m earlier in August but will want to add further defensive as they look to resolve their defensive woes and mount another title charge next season.
Napoli had hoped to bring in Gabriel Magalhaes as Koulibaly’s replacement but the left footed defender seems to be on his way to Arsenal.
However, they may have to turn their attention to other targets.
Gunners’ defender, Shkodran Mustafi and Shakhtar Donetsk man Mykola Matviyenko are both in contention, with negotiations underway with the latter also targeted by Leeds.
The proposed addition of the senegalese to City’s defence looks to be an exciting one as Guardiola plans to work on his defensive shortcomings in his team ahead of the new season.