The French centre-back is widely regarded as one of Europe's best defenders and has previously attracted interest from Manchester United, as noted by French football writer Jeremy Smith:
Varane joined Real Madrid in 2011 from French side Lille and has enjoyed great success with Los Blancos, winning La Liga, the Copa del Rey, four UEFA Champions League titles and the FIFA Club World Cup.
Varane has previously spoken about reported interest from the Red Devils when Jose Mourinho was at the helm of the club.
He told Spanish radio programme El Larguero (via AS) he had not spoken to United but there had been interest: "No, not directly [from Mourinho]. There were contacts, but not directly."
Real Madrid have already moved to strengthen their defence for next season by announcing the signing of Eder Militao from Porto for €50 million (£43.5 million) on a six-year deal, per the Guardian's Marcus Christenson.
The 21-year-old's arrival at the Bernabeu will leave the club with plenty of options at centre-back, as noted by Dermot Corrigan at ESPN FC:
Meanwhile, Manchester United are in need of a top quality centre-back to strengthen their defence. Victor Lindelof has emerged as first choice this season but needs a long-term partner.
The club do have plenty of centre-backs in the squad in Eric Bailly, Marcos Rojo, Phil Jones and Chris Smalling. However, none are at the elite level needed if United are to taste glory in the Premier League and UEFA Champions League.
The Red Devils have been linked with other centre-backs, including Napoli's Kalidou Koulibaly. Club chairman Aurelio De Laurentiis said he rejected a £95 million (€106 million) bid from Manchester United, per Goal.
Ole Gunnar Solskjaer's side also remain interested in a move for Tottenham Hotspur's Toby Alderweireld, according to Darren Lewis at the Mirror.
Manchester United appear to have the financial might to spend big on a defender, and the latest report concerning Varane could see the Red Devils revive their interest in the World Cup winner.
The 25-year-old is an elegant, skilful centre-back with plenty of experience and bags of pace. His exploits last season with Real Madrid and France saw him finish seventh at the 2018 Ballon d'Or:
Varane would not come cheap if he were to become available in the summer. However, he has the potential to become the cornerstone of the Manchester United defence, which may be enough to tempt the Red Devils into splashing out.