Perez was speaking at a hastily arranged media conference on Monday to give his backing to coach Rafael Benitez in the aftermath of the chastening 4-0 Clasico defeat to Barcelona at the Santiago Bernabeu on Saturday.
Reports that Benitez enjoys an uneasy relationship with Madrid's record goal-scorer Ronaldo has compounded the pressure on the former Liverpool and Napoli boss and fuelled suggestions that the three-time Ballon d'Or winner will seek pastures new.
Although he did not offer assurances over Ronaldo's long-term future, Perez insisted that he had no knowledge of a rift between coach and star player, while he lambasted claims that he had dinner with PSG president Nasser Al-Khelaifi and Ronaldo's agent Jorge Mendes last week.
"I don't know if you are capable of being sure that you're going to still be working where you work in a few weeks' time," Perez told reporters.
"I believe sincerely that there are people who lie in order to damage Real Madrid.
"Cristiano Ronaldo has never said anything about anyone. He has never said to me that with Rafa Benitez we aren't going to win anything."
Perez added: "The report that I had dinner with PSG president and Jorge Mendes last Thursday in Madrid is not true.
"It was an attempt to destabilise the club. The players support this coach and the board of directors too.
"From this point onwards I am not going to allow people to keep lying in order to destabilise the club."
Benitez and his squad travel to Shakhtar Donetsk for a Champions League match on Wednesday before returning to La Liga action at Eibar on Sunday, by which time Barcelona could be nine points ahead of them.
Madrid drawing a blank in the humiliating Clasico loss means Ronaldo is now without a goal in three matches.
The 30-year-old has 13 goals in 16 appearances for Madrid this season, although eight of those came in consecutive matches against Espanyol and Shakhtar in September.