Mourinho left Madrid after three seasons back in 2013.
The Portuguese won La Liga in 2012 but dressing room clashes with the likes of Cristiano Ronaldo, Sergio Ramos and Iker Casillas ultimately cost him his job.
However, Mourinho still has a close relationship with club president Florentino Perez.
Spanish outlet Don Balon claim Perez called the United boss to wish his wife well after a recennt health scare.
Jose Mourinho is in contact with Real Madrid chief Florentino Perez
However, their close relationship has fuelled talk Mourinho could one day return to the Spanish capital.
Despite Madrid sitting at the top of the La Liga table, Zinedine Zidane's future is reportedly – and somewhat amazingly – in doubt.
Their Copa del Rey exit to Celta Vigo last night means their dreams of the treble are now dead.
Hit or miss? Jose Mourinho's Chelsea and Manchester United signings since 2013
Tue, November 8, 2016
Jose Mourinho has made 24 signings since returning to the Premier League with Chelsea in 2013, but how many of them have been a success?
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Express Sport rates Jose Mourinho’s signings since arriving back in England with Chelsea in 2013, but how many have been hits and how many missed the mark?
Should their season begin to unravel then it is reported Mourinho is a potential candidate to take over.
Madrid know he is happy at United for the time being but, should their season fail to meet expectations, a sensational return further down the line could be on the cards.
That could come in the future with Mourinho traditionally staying for around two to three years at a club before leaving for a challenge elsewhere.