If that is the case, it is unlikely that the Portuguese will be given much freedom in the upcoming January transfer window.
But Los Blancos are 11 points behind Barcelona and five behind Atletico, so even confusion over Jose's future is unlikely to limit speculation on comings and goings.
So what business are Real Madrid likely to be involved in?
He may be approaching 150 caps for his country and may have amassed over 500 appearances in over a decade as Madrid's No. 1, but even Iker Casillas' position comes under threat at times.
With Antonio Adan as the current backup, speculation is heating up over who could be the heir to San Iker's throne.
TalkSport recently reckoned that Bayern Munich and Germany's Manuel Neuer, not de Gea or Courtois, would be the preferred choice should Mourinho seek a new goalkeeper.
In reality, it is unlikely that any of those three will be signing in at the Bernabeu in January. Much more likely to arrive would be a lesser-known goalkeeper to play second fiddle to Casillas.
With Fabio Coentrao and Marcelo, when both fit, providing healthy competition for the left-back slot, it is much more likely that Real Madrid will seek a right-back in January.
Alvaro Arbeloa remains their first, and possibly only real, choice at that position. But he's often a victim of criticism, which has led to a number of names linked with replacing him.
Borussia Dortmund's Lukasz Piszczek remains the favorite, with the player himself not even taking a recent opportunity to distance himself from a move to Spain.
With the German's progress in the Champions League, though, a January switch seems unlikely. But keep an eye on this one next summer.
Centrally, Mourinho seems happy enough with Sergio Ramos and Pepe's partnership, with Raphael Varane providing cover and, at times, rotation.
That leaves Ricardo Carvalho and Raul Albiol as a surplus to requirements, and should either move on, Marseille's Nicola N'Kolou is being tracked as a replacement.
The additions of Luka Modric and Michael Essien toward the end of the last transfer window leave Real Madrid well covered in midfield.
That hasn't prevented stories surfacing recently of a move for Roma's Daniele De Rossi, although PSG may prove a more realistic destination for the Italian.
It would be impossible to list every possible destination, as it has become a favorite pastime at every transfer window for Kaka to be touted to various clubs.
An interesting name to be linked with a move to the Spanish capital recently is Manchester United striker Javier Hernandez.
Robin Van Persie and Wayne Rooney appear to be Sir Alex Ferguson's preferred pairing, and it has been suggested that Real Madrid could force the Mexican to make a difficult decision (h/t The Sun): Stay or go.
It would seem unlikely, though. With only one central striker position available, Karim Benzema and Gonzalo Higuain have more than enough firepower to play that role in a side that already includes the goals of Cristiano Ronaldo.
Were either Benzema or Higuain to decide that they would be better suited, or loved, somewhere else, there would be no shortage of takers.
Then, as an alternative to Hernandez, comes Luis Suarez. More or less Liverpool's only goal scorer this season, the Uruguayan is likely to seek a move away from Anfield, either in January or the summer, as he seeks Champions League football.
And if he does? Well, the Daily Mail suggest that Real Madrid will be at the front of the queue.