The Old Trafford outfit have reportedly agreed a £42m fee with Real Madrid for the French defender, who has one year left on his contract in the Spanish capital.
If United are able to get the deal over the line, they will be bringing in one of the most experienced and decorated centre backs in the game.
Varane joined Real Madrid from Lens in the summer of 2011, and the 28-year-old has enjoyed enormous success with Los Blancos, winning four UEFA Champions Leagues, three La Liga titles and a host of other trophies. He also won the 2018 FIFA World Cup with France in Russia.
"When you watch him sometimes he almost purrs, he's got that pace, that poise," Ferdinand, who won six Premier League titles and one Champions League with Manchester United, said on his self-titled 'Rio Ferdinand Presents FIVE' YouTube channel.
"We've signed a genuine world-class centre-back. His list of honours is ridiculous, it's as long as my arm."
"What a signing. There's been talk in the transfer market since it opened up – it must have come from the player," Ferdinand continued.
"He must have wanted to leave, and be part of the new Man United way, the project that's going ahead.
"The talent they've got there, the ability to play alongside 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."