Speaking to Spanish radio programme El Larguero (via AS), Varane said he has never been contacted by the United manager with regard to a switch to the 20-time English champions but noted the club has shown an interest: "No, not directly [from Mourinho]. There were contacts, but not directly."
Varane, 24, joined Real from French club Lens in 2011 ahead of Mourinho's second season in charge at the Santiago Bernabeu.
Despite only being a teenager when he moved to Real, Mourinho gave the defender plenty of opportunities.
In his two seasons under the Portuguese, he played 24 times in La Liga and made 15 appearances in the UEFA Champions League.
The centre-back has previously spoken of the "special relationship" he enjoyed with Mourinho, a factor that has often been used to link Varane with a move to United, per L'Equipe (via Ben Nagle of MailOnline).
Following Mourinho's departure from Real in 2013, Varane's progress stalled slightly, but he is a regular in the Real first team under Zinedine Zidane and has started 20 of their 28 Liga games this season despite suffering a couple of injuries.
Given he is only 24 and a long way from his peak years, Varane is a supremely talented centre-back and would be a phenomenal addition to United's back line, which is overly reliant on the likes of Chris Smalling and Phil Jones.
However, while United may have made contact in the past and would surely like to move for Varane again, it seems unlikely he would be open to leaving the Bernabeu or that Real would be happy to see him go.