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.
Club president Florentino Perez took the rare step of entering the fray on Monday to call for unity for the last three weeks of the season, but Mourinho ignored his request and spoke out against Casillas and Pepe again on Tuesday.
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.
The 50-year-old has done little to quash the rumours of his possible return to former club Chelsea, while his public attacks on Casillas and Pepe have been interpreted as further evidence that his time in Madrid is nearing the end.
"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."
