While United have been linked with the centre-back for a number of transfer windows, a deal is yet to come close to fruition.
However, Corriere dello Sport claims that Napoli are prepared to lower their asking price for the Senegal international.
The report says that president Aurelio De Laurentiis now values Koulibaly at £85m and is not prepared to consider any other fee for the 28-year-old.
When United and other clubs have been credited with an interest in the past, it has been suggested that Napoli would demand in excess of £100m.
Koulibaly still has over three years remaining on his contract at Stadio San Paolo.