United boss Jose Mourinho is believed to be desperate to sign a new central defender this summer, and the 20-time English champions have been strongly linked with a move for Tottenham Hotspur's Toby Alderweireld.
However, according to TMW, Koulibaly is also on the club's wishlist ahead of the 2018-19 campaign.
That said, the same report claims that Napoli value the 26-year-old 'in excess of £70m', which is just shy of the figure that Liverpool paid Southampton for Virgil van Dijk during the January transfer window.
Koulibaly, who has a contract with Napoli until the summer of 2021, is currently with Senegal at the 2018 World Cup.
Chelsea have previously been linked with a £65m move for the former Genk defender.