The nine-times European champions host Malaga in La Liga on Wednesday (1930 GMT), in a rearranged fixture due to their involvement in the May 17 King's Cup final against Atletico Madrid.
Second-placed Real must win to make leaders Barcelona wait to be crowned champions, as they trail Tito Vilanova's side by 11 points with four games left.
Anything less than a victory would gift Barca a fourth league crown in five years without having to play.
Speculation over Mourinho's future has gone into overdrive since Real were denied a place in the Champions League final by Borussia Dortmund last week, and the Portuguese has done little to quash it.
Instead, Mourinho stirred up simmering divisions at the club last Friday by having a dig at popular club captain and goalkeeper Iker Casillas who he has dropped in favour of Diego Lopez recently.
The Bernabeu cheered Casillas's name when it was read out among the substitutes at the stadium before their 4-3 league win over Real Valladolid on Saturday. Mourinho's name was whistled by a large section of the crowd.
Pepe, a player regarded as a Mourinho favourite, and Sergio Ramos have since made comments in support of Casillas in local media.
"We have two big challenges in front of us with the Euroleague (basketball) Final Four and the King's Cup final," Perez told reporters on Monday.
"We should be united for the fans, and give our all. Our players will do that."
Real's league challenge is effectively over but they defend a 42-match unbeaten record in all competitions at the Bernabeu against a side suffering similar end-of-season symptoms, Malaga.
Since their Champions League quarter-final exit, also to Dortmund, Manuel Pellegrini's side have steadily slipped out of contention for a top-four finish.
The Costa del Sol club are sixth with 53 points and are beset by rumours over the future of coach Pellegrini and possibly even their Qatari owners.
"We have to finish the year well so as not to spoil the season we have had," Malaga's Brazil forward Julio Baptista told reporters.
"It would be a shame not to get the points that would earn us a place in Europe.
"Although it is tough, we must forget about what is happening off the pitch. There are lots of non-football related issues, but the most important are the football ones."
Third-placed Atletico visit relegation-threatened Celta Vigo on Wednesday (1730) looking to make the last automatic qualification berth for the Champions League mathematically safe.
- Sports & Recreation
- Iker Casillas
- La Liga
- Tito Vilanova
- Borussia Dortmund