Madrid lost 2-1 away to Borussia Dortmund on Wednesday, and head to the Iberostar Stadium with little room for further error if they are to keep within striking distance of pacesetters Barcelona and Atletico Madrid.
However, a third La Liga defeat would see Mallorca move level with Mourinho's side, who head into the weekend's games down in fourth place, some eight points off the top already.
Midfielder Sami Khedira will not be available after he limped off against Dortmund, so Croatian Luka Modric could come into the starting XI or Michael Essien may move up from left-back, where he has been filling in because of a defensive shortfall.
Mourinho is confident his team can return to winning ways having recovered from a terrible start to the new campaign.
"We are not used to having so many defeats at the start of a season, but we need to take a look at the matches. Dortmund played more tightly than we did," he said.
"We have matches in league and cup coming up and we need to go and win those."
Full-backs Alvaro Arbeloa and Fabio Coentrao are continuing their rehabilitation from injury, but are not yet back in full training.
Mallorca had made a solid start to their season, but head into Sunday's game looking to arrest a run of three successive La Liga defeats.
Mexican forward Giovani dos Santos made his debut in the 3-2 defeat at Sevilla, having a hand in both goals during a match in which the Balearic Islanders twice led.
The former Tottenham man, 23, is hoping to develop his game with Mallorca.
"It is clear that I will get a lot better as long as I keep getting more time on the pitch, I know that," Dos Santos told the AS newspaper.
"I know that I still need to improve."
On-loan Barcelona central defender Andreu Fontas was another debutant last week and is relishing the chance to take on Madrid.
He said on the Mallorca website: "Real Madrid is always a special opponent for me because of my past and also we are all keen to play against this great team.
"Madrid come with even more motivation and desire to win.
"We must work as a team knowing that we face a very difficult opponent.
"We must stand up and take our chances."