The Red Devils could do with strengthening at the back this summer, with Varane perhaps ideal after a great career at the Bernabeu.
The France international has won almost all there is to win in the game, playing a key role for Real in their four recent Champions League title successes.
United would surely view Varane as an upgrade on Victor Lindelof and Eric Bailly, neither of whom has really done enough to look like the best long-term partner for Harry Maguire in the United defence.
Butt is certainly a fan of Varane, and has named the 28-year-old as an ideal signing for his old club this summer.
The former MUFC midfielder, speaking exclusively to Ladbrokes at the launch of their European Championships 5-a-side Bet, said: “For me, next season has to be about getting some silverware back in that trophy cabinet for Manchester United. It’s about getting the right players who will allow you to challenge for trophies. It’s a winning club, so we can’t go this long without silverware.
“The biggest thing that needs addressing for me at Manchester United this summer is that centre-back position; we need a partner for Harry Maguire. It has to be someone that’s going to be compatible with Maguire.
“If you spend the kind of money you did on Harry Maguire, you then have to follow it up by bringing someone in who can play with him. He’s the club captain; Victor Lindelof is too similar to him. It needs to be someone with pure, blistering pace, someone who can play out from the back.
“Everyone talks about Raphael Varane. I understand he’s a little bit older than most people would perhaps like, but you just have to go back to the days of Teddy Sheringham. I think we bought him when he was 32, and we went and won the treble with him. If Varane is available, then I’d go all out for him.”
Varane is heading towards the final year of his Madrid contract, so could be a perfectly realistic target for Man Utd and other big clubs this summer.