It comes as the Red Devils find an agreement with Real Madrid over the signing of the centre-back – who looks set to sign for a fee rising to £42m.
Ole Gunnar Solskjaer has been desperate to sign a defender in the transfer window to partner Harry Maguire.
And even the Norwegian might be pinching himself to land one of the best in the world for a relatively modest amount.
Varane will enter the Old Trafford dressing room with immense pedigree having won the Champions League four times, as well as the World Cup.
The Frenchman has played alongside some of the biggest names in football including Sergio Ramos, Kaka and Paul Pogba.
But none come close to Ronaldo, who he won four Champions League titles with while at the Bernabeu.
The Portugal international has a close affiliation with United, where he became a major star and won the Ballon d’Or for the first time – one of five.
And Ronaldo has already told fans what to expect of Varane at Old Trafford while also giving his blessing.
Eight years ago, the France international was an up and coming talent at the Bernabeu having joined from Lens as an 18-year-old in 2011.
As he started to break into the first-team in 2013, Ronaldo revealed he saw the defender becoming one of the best in the world – prediction that has since come true.
“Varane is now learning a lot. He has grown as a player and as a man,” Ronaldo said in 2013.
“He is quick, he has good composure and he is very calm.
“He is accumulating experience at his young age. He is humble and, for me, in a few years will be one of the best central defenders in the world. I have no doubt about it.”
Varane is set to become the second signing of the summer at United following the arrival of Jadon Sancho earlier in the window.
But there are further plots planned for the likes of Kieran Trippier and Eduardo Camavinga.
Solskjaer is determined to sign four players and has completed half of the job so far with a midfielder and a right-back also on his wish list.
There is also plans to bring in a striker but it is not seen as urgent following Edinson Cavani’s contract renewal while the likes of Harry Kane and Erling Haaland are too expensive for this summer.
Both have been priced at over £150m – an unattainable sum considering the other players being brought in.