Despite challenging Barcelona for the La Liga title, Mourinho has come under fire recently from Real fans and Spanish media alike.
This has sparked rumours that the Portuguese will quit Real at the end of the season, most likely for a return to the Premier League.
The press conference, ahead of Wednesday night's Copa del Rey quarter-final second leg away to Barca, did little to dispel the feeling Mourinho is unhappy in Madrid.
When asked about the unsourced report that he plans to leave, Mourinho said: "Did I say that? Ask your colleague." And when the subject changed to whether he is happy at Real, he merely shrugged.
Mourinho's relationship with the Real hierarchy is already strained, having previously stated he wants to return to England "in as couple of years".
On Tuesday night, 'The Special One' wound up his employers even further by saying: "I don't know if I will be at Real Madrid next season."
Should Mourinho decide enough is enough and walk away from the Spanish giants, Real have reportedly already drawn up a two-man shortlist to replace him, and on it are the names of Wenger and Germany national team coach Joachim Loew.
Wenger has been linked with Madrid for the past few years and turned down the chance to move there in 2009.
However, with Arsenal no longer the force they once were in England's top flight, Real believe now is their best chance to lure the Frenchman away from north London and to the Spanish capital.
Real Madrid 2-1 after the first leg.