Mourinho's recent decision to drop captain Iker Casillas was met with widespread disbelief in Madrid and came with Real well adrift of Barcelona in La Liga.
But Perez called a press conference to deny reports a meeting with Casillas and senior defender Sergio Ramos was anything more than routine.
He said: "I'm speaking in light of the seriousness of what happened in order to make it clear that there was no ultimatum that the coach or anyone else leave the team.
"We had lunch to discuss bonuses. The meeting was held in a relaxed atmosphere as usual. What has been said is not true, not in its content or in how much was said.
"Given the seriousness of this, I've broken my own rule about not speaking about day-to-day team business."