Varane joined Madrid in 2011 and he enjoyed a promising start to life at the Bernabeu under current Man United boss Jose Mourinho but he found chances harder to come by when the Portuguese left.
Zinedine Zidane dropped Varane for crucial games in the Champions League towards the end of the 2015/16 campaign, instead preferring Sergio Ramos and Pepe.
Although Zidane is said to be keen on keeping Varane, the 23-year-old is considering leaving Madrid.
Man United have already completed the signing of Eric Bailly from Villarreal this summer but reports have suggested that Mourinho wants to add another central defender to his squad and Varane would fit the bill.
United could certainly offer him a lucrative contract and a regular spot in the starting XI but it is unclear whether Varane would accept not playing in the Champions League. But if Varane is available, Mourinho should be doing all he can to bring him in as he is a top talent who would add quality depth to the squad.