According to La Repubblica (h/t the Mirror's Jack Rathborn), Napoli chief Aurelio De Laurentiis did not hesitate to reject the bid, as he is hoping for a fee in the region of €100 million (£89 million).
Per Rathborn, Koulibaly only signed a new deal in September to tie him down until 2023. There's said to be plenty of competition to prise him away from Naples, too, as Europe's other elite sides such as Real Madrid, Barcelona, Bayern Munich and Manchester City are also interested.
It's little wonder Koulibaly is attracting so much interest, as he has become one of the world's best defenders since joining Napoli in 2014.
He's very strong and has an impressive turn of pace for a centre-back, too.
He's not just a supreme athlete, though. The 27-year-old often nullifies threats before they happen and also developed the technical side of his game under former Partenopei boss Maurizio Sarri. He thrived in the Italian's system, which required him to carry the ball out from the back.
Italian football experts David Amoyal and Matteo Bonetti are big fans of the defender:
Matteo Bonetti @TheCalcioGuy
I can’t think of any centreback I’d pick ahead of Kalidou Koulibaly. At nearly 6’6 (198cm) he’s always a threat from set pieces. Add to that his reading of the game, and his improvement in possession thanks to Napoli’s style. This man is world class. #SEN https://t.co/evu0LOgM7p
Koulibaly has offered a reminder of his talents in the UEFA Champions League this season, helping Napoli beat Liverpool and twice hold Paris Saint-Germain to a stalemate.
Even Kylian Mbappe found him to be an insurmountable obstacle:
He'd be an outstanding capture for virtually any side in Europe, and United are no exception.
The Red Devils are paying for not improving their centre-back options in the summer, keeping just one clean sheet in their first 12 Premier League games.
United's problems are partially organisational, which will require work on the training ground rather than in the transfer market to resolve, but Koulibaly would be a significant upgrade on any of their centre-backs.