The Senegalese defender has attracted attention from all across Europe with his impressive displays for Napoli in recent years.
But the price-tag that the Serie A side has placed on Koulibaly has deterred some suitors.
Napoli are understood to want around £90m for their prized asset.
United were believed to prioritise the signing of Harry Maguire last summer, which was a deal done for £80m.
But now United are reportedly ready to dig deep into their pockets once again, this time for Koulibaly.
Ole Gunnar Solskjaer is thought to be convinced that the 28-year-old would be the perfect partner for Maguire in the heart of United's defence.
The Red Devils have apparently been made aware that Koulibaly is open to a move to England.
Solskjaer's determination to bring the defender to the club is such that he has reportedly encouraged the board to make him the highest-paid player at the club.
It's unclear what such a move would mean for United defender Viktor Lindelof, who has built a partnership with Maguire this season.
Solskjaer will be hoping his new signings, Bruno Fernandes and Odion Ighalo, make a difference in the latter half of the season.
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