The position is one of three that manager Jose Mourinho still wants to enhance this window, along with a top priority defensive midfielder and a winger - although he would also like to sign another striker if the opportunity presents itself.
Fabinho has been United's top target for the right-back position but, in what has become something of a trend of the summer, Monaco have proven exceptionally tough negotiators as they aim to get as much money as possible for the interest in their talented young squad.
Their hand is also strengthened by the fact that Atletico Madrid and Paris Saint-Germain are interested in the player, potentially raising his price past £40m, although Monaco would prefer to sell to a club outside France.
With a deal proving difficult to finalise, United have already started looking into the possibility of signing 24-year-old Aurier.
Any purchase would not necessarily be dependent on PSG buying Fabinho, since they don’t primarily see him as a right-back.
The Ivorian international would also be cheaper than Fabinho and could feasibly be signed for £25m.
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