The French centre-back is close to securing a move to Old Trafford after the two clubs reportedly agreed a £41m deal.
With a deal likely to go through in the coming weeks, Ferdinand believes Varane approached Real and demanded an exit this summer.
Ferdinand said during a video on his YouTube channel: "What a signing. There's been talk in the transfer market since it opened up - it must have come from the player.
"He must have wanted to leave, and be part of the new Man United way, the project that's going ahead.
"With Ole Gunnar Solskjaer signing a new deal, Sancho coming in - the talent they've got there, the ability to play alongside (Harry) Maguire after he did so well at the Euros probably played a part. I just think he sees this as a better project than what he's got at Real Madrid now.
"When you watch him sometimes he almost purrs, he's got that pace, that poise. We've signed a genuine world-class centre back. His list of honours is ridiculous, it's as long as my arm.
"It's a great job by the (recruitment) people at Manchester United. United have been criticised in the past, and rightly so, for dilly-dallying in the market.
"This one they were assertive, they went for their man and they got him. No doubt in my mind, he would have said to Real Madrid 'I need it, I want it, I have to go."
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