The nine-times European champions visit Espanyol on Saturday when a failure to win would gift leaders Barcelona their fourth La Liga title in five years.
Even if they do triumph, Barca only need two more points to secure the trophy, which they could achieve at third-placed Atletico Madrid on Sunday.
Mourinho's dig at captain and goalkeeper Iker Casillas a week ago, followed by defender Pepe's subsequent defence of his team-mate last Saturday, has brought divisions within the dressing room to the fore.
The Bernabeu crowd cheered Casillas' name when it was read out among the substitutes before the 6-2 La Liga victory over Malaga on Wednesday, while Mourinho's was met with whistles and jeers from a large section of the stadium.
After the game, Spanish internationals Xabi Alonso and Raul Albiol both appealed for club unity ahead of the King's Cup final against Atletico Madrid on May 17th, which will be the side's last chance for major silverware this season.
Mourinho's future in the Spanish capital, despite him having a contract until 2016, has been the subject of a great deal of speculation since Real failed to reach the Champions League final last week.
"Perhaps now is the moment to say enough, to move on from the controversies with the boss, with Iker, with Pepe," Real defender Sergio Ramos, a senior figure in the squad, told Spanish broadcaster La Sexta at the Madrid Open tennis tournament on Thursday.
"It's a question of thinking only about the final which is the most important thing, and of trying to win it.
"Let's leave behind the controversy and the individual egos and focus on the union of the team which is fundamental, and without which success is impossible."
