The Portuguese is enduring a tough third season in charge at Old Trafford as United are currently eight points off fourth-placed Arsenal, who they will face tonight.
Similarly, Real are also struggling domestically. The Spanish giants replaced manager Julen Lopetegui with Santiago Scolari in October.
Despite Scolari signing a two-year deal, it is no guarantee Real president Florentino Perez would replace him at the end of the season if the right manager became available.
Mourinho would be that man, and according to the London Evening Standard, the feeling is mutual.
'The Special One' was in charge at the Bernabeu for three years before leaving in 2013, but has maintained a good relationship with Perez and would be open to a return.
He is under contract at United until 2020, but if similar results continue, the club will be forced to take action.