Koulibaly's future in Italy has been unclear for 12 months or more with Manchester United and Barcelona both reportedly keen on the 28-year-old centre-back.
Only last month Calciomercato claimed Ole Gunnar Solskjaer wanted Diego Godin to be joined by Koulibaly this summer.
According to Area Napoli, the Serie A giants have made the decision that there is no room for the likes of Koulibaly, Allan and Hirving Lozano on their books and one or more will be sold in the next window.
Now Mundo Deportivo claim PSG have moved ahead of United and Barca for the Senegal international after agreeing a price in principle with Napoli chief Aurelio De Laurentiis.