Koulibaly's future has been the subject of speculation for some time but Napoli have so far managed to resist any offers that have come in for the centre-half.
However, Naples-based publication Il Mattino says he has told club president, Aurelio De Laurentiis, he is open to a move away - but he would also be happy to stay at Napoli if no suitable offers are received.
The Italian outfit may well be ready to cash in on their star man in order to fund a squad overhaul but previous reports have indicated the Partenopei would demand a fee in excess of €100 million for the 28-year-old, who is under contract with the Serie A club until 2023.
A host of Premier League clubs have been linked with Koulibaly in the past but at present Manchester United appear the most likely English outfit to come in with a concrete offer.