Real's surprise 2-2 draw at home to lowly Espanyol on Sunday left them four points behind second-placed Atletico Madrid and a whopping 13 adrift of unbeaten leaders Barcelona after only 16 games.
The champions have already dropped more points than they did in the whole of last year's record-breaking championship campaign and a deflated Mourinho said after the Espanyol game that the title was "almost impossible now."
On Saturday, Real president Florentino Perez, who brought Mourinho to the club in 2010, backed his Portuguese coach to the hilt but on Monday he fired out what sounded like a rebuke.
"Real Madrid has a sporting principle that one should never give up, however difficult the challenge," he said at a club event.
Perez and Real's fans have a notorious shortage of patience and a failure to win would have the vultures circling going into the two-week winter break, with their desire to win the Champions League the main reason for holding off more drastic action until later in the campaign.
Pellegrini knows Mourinho's situation all too well.
In his trophyless year at the Bernabeu in the 2009-10 season he set a then club record tally of 96 points in La Liga only to finish second behind Pep Guardiola's Barca, and he was unceremoniously ditched in favour of Mourinho.
The calm, silver-haired Chilean, known as 'the engineer', is a striking contrast to his brash, outspoken successor and there is little love lost between the two.
Mourinho's belittling dig at Pellegrini a year ago, when he said he would never go and coach a team like Malaga but would instead leave Real to go and take the helm at a big club in England or Italy, did little to endear him to the locals either.
Pellegrini has stuck to his guns, however, and guided them to fourth in La Liga last season, their highest ever finish which earned them a first ever shot at the Champions League.
Despite the loss of players such as Santi Cazorla, who was sold to Arsenal, and problems with the payment of squad wages, Malaga qualified for the last 16 in Europe as leaders of their group ahead of AC Milan.
Their attractive passing game and solid defence, currently the tightest in La Liga with only 10 goals conceded this season, has put them in fourth on 28 points level with Real Betis and five points behind Mourinho's team.
Real have struggled on the road and have striker concerns with Gonzalo Higuain still sidelined while out-of-form Karim Benzema is a doubt with a foot problem.
The game throws up a clash of styles just when Mourinho's counter-attacking tactics are being questioned the most.
"Madrid cannot be a team who runs behind the ball..with players of that category and standing," Pellegrini said in a recent interview.
"I don't like coaches who are only interested in results. The concepts of spectacle and creativity are fundamental to me."
Barca could increase the pressure on Real and move 16 points clear of their arch-rivals with their 16th win in 17 league games if they can overcome Valladolid away on Saturday (1700) before the match at the Rosaleda kicks off (1900).
Second-placed Atletico close out the year at home to promoted Celta Vigo on Friday (2100).