Koulibaly’s agent Fali Ramadani visited Naples on Friday and has since held talks with Napoli owner Aurelio De Laurentiis.
And Ramadani confirmed the interest of Pep Guardiola’s side for Senegal defender Koulibaly.
However, City are unwilling to spend the €75m (minimum) that Napoli want.
Napoli have dropped their asking price from €100m but €75m-plus is still big money for a 29-year-old.
City have been thinking of a fee more in the region of €50m plus bonuses.
The market is still in its early days and anything could happen, but a deal for Koulibaly to join City is complicated.
The player himself has expressed a wish to retire in Naples and therefore is unlikely to agitate for a move.
Any deal for Ake would not necessarily rule out Koulibaly, with City potentially looking to add two central defenders.