United are getting closer to a deal for Varane, who is expected to cost around £50 million.
The 28-year-old has four Champions League titles with 'Los Blancos,' as well as a World Cup title with France.
However, talkSPORT's Jamie O'Hara believes Stones is better than Varane, who he believes would not be leaving Real Madrid if he were that good.
"I love John Stones, I've always liked him. He's a brilliant football player," he explained.
"He's the closest thing we've had to Rio Ferdinand, who along with John Terry, was the best centre-half in the Premier League.
"I love watching John Stones, I enjoy watching the way he plays. He's calm, he's composed but also a brilliant defender.
"Last season you had Ruben Dias alongside him which turned him into an even better defender because he had someone with him.
"I think with Varane he's going to have that with [Harry] Maguire but in my opinion I'd rather have John Stones in my team.
"If Varane's that good, why is he leaving Real Madrid at 28 years old? Why not give him a new deal? If they thought he was that brilliant they wouldn't be letting him leave. Manchester City aren't letting John Stones leave..."
Stones was a standout for England at Euro 2020, helping his country reach the final. City won the Premier League and Carabao Cup last season, as well as reaching the Champions League final.
Varane, meanwhile, went trophyless during his time at Real Madrid, where he parted ways with manager Zinedine Zidane.