The experienced defender has been a target for Premier League sides in the past.
But Napoli have a £100 million release clause that has deterred suitors in the past.
90min now reports that Pep Guardiola's City may be willing to pay the clause.
City want a top level centre-back who can partner Aymeric Laporte, as they have struggled in defense this season.
Koulibaly is 28 but is still expected to have several years at the very top in him.
And the Daily Express reports that West Ham may also have an interest in Koulibaly, although a move to the Hammers is unlikely to appeal to the player.