After some unsavoury sniping between Mourinho and members of his squad in recent weeks, Perez made a rare foray into the limelight on Monday when he called for the club to be "united for the fans" as they prepare for this month's Copa del Rey Cup final against city rivals Atletico Madrid and seek to secure second place in La Liga.
Mourinho raised eyebrows on Friday when he made a thinly veiled attack on goalkeeper Iker Casillas, whom he has dropped in favour of Diego Lopez, prompting club heavyweights Sergio Ramos and Pepe to speak out in support of their captain.
The sense that all is not well has been heightened by speculation that Mourinho is poised to leave at the end of the season and the outspoken Portuguese has said little to contradict reports he is on his way back to Chelsea.
At a news conference on Tuesday previewing Wednesday's La Liga match at home to Malaga, he responded to Portuguese compatriot Pepe's expression of support for Casillas, made after Saturday's 4-3 La Liga victory at home to Real Valladolid.
Pepe had spoken out because he was frustrated that team mate Raphael Varane had edged ahead of him in the pecking order to partner Ramos in central defence, Mourinho said.
"You just have to be a normal person like me or like almost everyone in this room to know that we are talking about frustration," he said.
"His problem has a name: Raphael Varane. It's not easy for a man of 31 years, with status and history, to be trampled over by a kid of 19.
"But that's the law of life. On a sporting level Pepe's life has changed.
"I have no problem with him. I understand that it's not an easy situation but I have to try to be honest and I think that there are very few people who don't think that the future of Real Madrid in defence is Varane with Sergio Ramos."
Asked about his relationship with Casillas, Mourinho reiterated that he believed Lopez, who was brought in ostensibly as cover when Casillas broke a bone in his hand in January, was the better keeper.
Casillas has been Real and Spain keeper for more than a decade and is a hero to fans of the club and the national team.
"Let's see if you understand it once and for all, I am a soccer coach," Mourinho told reporters.
"They hired me to be a soccer coach and a soccer coach has certain responsibilities, one of which is to pick the team.
"I don't do it by flipping a coin. I do it after discussion and lengthy analysis of my decisions.
"For me, I like Diego Lopez better as a goalkeeper than Iker Casillas. I don't do it to harm anyone.
"I accept it if someone says that Casillas is better than Diego Lopez but you have to accept that I am the coach of Real Madrid."
Mourinho, who almost walked out of the news conference after repeated problems with the sound system, was again asked about his future at Real, where he has a contract until June 2016, and whether he was trying to provoke the club into sacking him so he could pocket a substantial payoff.
"So that there is absolutely no doubt, I want to say that I will earn a salary until the final day I work for Real Madrid," he said. "I don't want a single euro more."
If defending champions Real fail to beat Malaga on Wednesday, leaders Barcelona will have an unassailable lead and will secure their fourth La Liga title in five years.