Varane is believed to have obtained a visa to travel to England, where he will have to quarantine following his arrival.
The 28-year-old defender has agreed to join United in a deal that could rise to £43million, with the transfer subject to a medical.
Sources have described the process to complete Varane's move as 'annoyingly slow' after the France international bade farewell to Real Madrid players and staff last Friday.
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