The Mirror says United will offer Koulibaly an escape route away from Italy's racists.
United have made the 27-year-old Senegal international a prime summer target after failing to land him before the start of the season. And they believe Koulibaly will this time attempt to force his departure from the Serie A club after being targeted by bigots.
The issue has left Koulibaly devastated – and a move away from Italy now appears to be the most likely outcome.
Napoli president Aurelio De Laurentiis has ruled out the player's departure during the January transfer market. He has claimed to have rejected a £95million bid from United in the summer – a declaration that has been denied at Old Trafford.
But while United sources insist their interest in Koulibaly never went beyond making an enquiry about a valuation, they have made signing the France-born defender a priority.