The two clubs have only been communicating through Fali Ramadani, the defender’s agent, as the respective sides do not enjoy a good relationship.
The negotiations have dragged on for weeks as Ramadani went back and forth between the two clubs, trying to work out an agreement over a fee.
Manchester City offered to pay a package of €70m, plus hard to reach bonuses, but Napoli want more and the talks have since then been on ice.
And according to Italian broadcaster Sportitalia, there are no ongoing negotiations between the two clubs over Koulibaly’s proposed move to the Premier League.
Manchester City have turned their attention towards Atletico Madrid defender Jose Gimenez and have tabled a bid for the player.
The Premier League giants could even be ready to wait another season to land a top-class centre-back.
Koulibaly has a contract in place with Manchester City and is now been left in limbo with no clarity over his future.
It remains to be seen whether Manchester City look to rekindle the negotiations with Napoli in the coming days.
Napoli president Aurelio De Laurentiis has threatened to take the player off the market if a deal for his sale is not agreed by the end of the week.