The Daily Express reports he already follows several United players.
One is Paul Pogba, with the two both regulars for France at international level, with the pair having 150 caps between them.
It emerged after their exit from Euro 2020 the two had clashed but that's unlikely to stand in the way of United completing a deal.
Varane also follows Anthony Martial.
ABC reported over the weekend that the France international had a 'total agreement' with the Red Devils about a move.
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