Mourinho brought the France international to the Santiago Bernabeu while he was in charge of Los Merengues, although Real may not be keen on a deal if veteran Pepe leaves the club as expected this summer.
Sky Sports News' Rob Dorsett discussed the interest in Varane and the links between the player and former mentor Mourinho:
According to Sky Sports, Varane is a "key target" for Mourinho, who presumably wishes to pair the 24-year-old alongside last summer's star defensive signing, former Villarreal man Eric Bailly.
Marca's Chris Winterburn has cast some doubt over whether Los Merengues would be willing to sell a player who finally looks set for his chance to step out of Pepe's shadow, however:
It's also mentioned by Sky Sports that David De Gea, a long-term target for Real Madrid, could play a role in any deal that sees Varane move to Old Trafford, having come close to joining Los Blancos in the summer of 2015.
Samuel Luckhurst of the Manchester Evening News highlighted that while the deal is inevitably a difficult one, Mourinho could pull off a deal for Varane, who idolised United great Rio Ferdinand in his youth:
The defender has made 38 appearances this season and started in all but one of those outings. If Pepe leaves the club when his contract expires, his first-team prospects under manager Zinedine Zidane are looking up.
There's also the question as to whether Varane wants to leave the Bernabeu, particularly if he helps guide Real to a third UEFA Champions League title in four seasons when they face Juventus in Cardiff, Wales, on Saturday.
The Red Devils are only just preparing to make their return to Europe's elite competition after beating Ajax to this term's UEFA Europa League crown, and Varane may fancy his career prospects more so in Spain's capital.
Centre-back was always liable to be an area of focus for United during the summer transfer window, with the side left short during absences from Bailly, Chris Smalling, Marcos Rojo and Phil Jones over the course of the season.
It could be the English powerhouse will have to soften their stance on De Gea and his potential move to Madrid if they want to lure one of Europe's rising defensive forces from Spain, with Mourinho hunting a reunion in Manchester.