Jose Mourinho is keen to improve his defence ahead of Manchester United’s return to the Champions League.
Reports yesterday claimed they were closing in on a £35m deal for Victor Lindelof.
But Sky Sports now say they want Varane from Madrid.
The 24-year-old will try and win his third Champions League title on Saturday when Madrid face Juventus in Cardiff.
Raphael Varane is on Manchester United's radar Manchester United summer transfer targets Tue, May 30, 2017
Express Sport takes a look at who could be on Manchester United's shopping list this summer
Play slideshow Everton FC via Getty Images 1 of 15
But Mourinho, who worked with him at Real, hopes to seal a deal to bring him to Old Trafford.
United signed Eric Bailly last summer for £30m from Villarreal but Mourinho’s other defenders have struggled with injury and inconsistencies.
United are also targeting a striker although Antoine Griezmann is no longer the priority signing after it emerged Mourinho wanted a number nine type to replace Zlatan Ibrahimovic.
Varane joined Madrid signed for Real in 2011 from Lens and has 35 France caps.
With Madrid keen on David De Gea United may have bargaining power although Zinedine Zidane will not want to lose the defender.
Get Quotes on Home Insurance
Varane started 23 games in La Liga as Real secured the title on the final day of the season over rivals Barcelona.