The Mirror says Ferguson has already given his support for United to sign Varane.
Talks are ongoing between United and Real Madrid as the French defender is at the top of Ole Gunnar Solskjaer's wishlist following the confirmed arrival of Jadon Sancho from Borussia Dortmund on Friday.
Madrid are holding out for a fee of £50million for the centre-half, but Mirror Sport understands United are only willing to pay £40m with the stopper out of contract next summer.
United are hopeful Carlo Ancelotti's men will lower the asking price with the risk that he could walk for free in 12 months' time as they look for a long-term partner for Harry Maguire in the centre of defence.
It's a transfer that would have the seal of approval from legendary boss Ferguson as well who narrowly missed out on Varane's signature in 2011 as he opted to join the La Liga giants instead.
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