United have held talks with Varane about a possible £30m move.
The France international has fallen down the pecking order at Real and has struggled to hold down a starting place since Zinedine Zidane took charge.
But while he is open to joining United, the centre-back has made it clear he will pull the plug if ‘The Special One’ doesn’t become the club’s next boss.
Varane, who has 28 caps, is close to Mourinho, who signed him from Lens when he was boss of the Spanish giants in 2011.
He is willing to team-up with Mourinho once again, but has no interest in joining United if Van Gaal remains at the helm for one more season.