Manchester United lost 1-0 to Juventus in the Champions League in midweek to end their three-game unbeaten streak.
Results have been up and down at United this season and Mourinho is under pressure to get his team firing again.
He has been linked with a sensational return to Real five years after he left the Bernabeu – with Julen Lopetegui tipped to lose his job if Los Blancos lose to Barcelona on Sunday.
And former Real president Ramon Calderon reckons the Portuguese manager will soon return.
“If this president is with the team for a few years, and I think he will be, Mourinho will be here,” Calderon told ESPN.
“No doubt. It’s the only coach the president has respected.
“For better or worse. I think he will be here – if he leaves Manchester, of course.
“But sooner or later, I think he will be here.”
Mourinho ended up falling out with the Real hierarchy and, a year after winning the La Liga title in 2012, he was booted out.
But the manager is one of the frontrunners to join Real when Lopetegui is inevitably sacked.
Antonio Conte is the current favourite, with the former Chelsea boss still out of work.
However, Real would have to negotiate with Chelsea over the remaining eight months of Conte’s contract, which the Blues are still paying.
Arsene Wenger is also free but may not be too keen on taking up the Real post in these circumstances.
And Tottenham are determined to fend off any interest in their manager Mauricio Pochettino.
As for Lopetegui, Calderon is adamant the manager will get the sack imminently.
“Unfortunately, I think (Lopetegui) has been condemned (to the sack),” Calderon said.
“A few weeks ago the president thinks he is not the man to run the club.
“He’s been in touch with many coaches but it’s not by chance that (Zinedine) Zidane left and five important coaches rejected that bench.
“It’s because this president interferes very much with what is happening on the ground with the line-ups and the signing. That for coaches is always a problem.”