Liverpool this season have shown how important a top-class defender can be in transforming a side and United will be hoping that Koulibaly can have a similar impact to Van Dijk at Anfield, even if he costs over £100m.
Ole Gunnar Solskjaer will be consulted over United's targets and the club have not ruled out adding to their squad this month.
Koulibaly has always been linked with a move to the Premier League and he has been in good form for Napoli so far this season, making two assists in 21 Serie A games. Reports last month claimed that the 20-time English champions would launch a move for the Senegalese worldwide irrespective of who the manager of the club will be in the summer.
United would now need to smash the world-record fee for a defender if they want to sign him. Lawlor was reportedly impressed with Koulibaly as he featured in last Saturday's 0-0 draw at Fiorentina in the Serie A, as well as featuring in Napoli's 3-1 win over Zurich in the Europa League five days later.
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Till date, the 27-year-old man mountain has featured 194 times for Napoli - 30 of which have come in the 2018-19 season - scoring 8 goals and assisting 7 more.
The towering defender is approaching 200 appearances for Napoli, after joining from Genk back in 2014.
The Senegalese worldwide said that what he wants was to demonstrate on the field that he is at the level of the greatest defenders in the world. I always try to give my best.
Koulibaly has admitted he has been flattered by interest in him, saying: "I am pleased that many teams follow me".
Given Manchester United's struggles at the back, they would stand to benefit immensely with the addition of Koulibaly to their ranks.