Perez took the unusual step of responding directly to the speculation, branding the report an "attempt to destabilise the club" in a press conference convened at short notice at the Bernabeu this afternoon.
A short time later a joint statement from Casillas and Ramos was posted on the club's official website, in which the Spain internationals rejected the claims while affirming their support for both the club and Mourinho.
The statement read: "The two captains of Real Madrid want to communicate the following: 1. That the meeting held on Tuesday with the president and CEO of the club never raised any ultimatum from us regarding the character of our coach.
"2. As captains of the staff and members of an excellent group of people and professionals, we categorically reject the use of our names and the rest of our squad's in support of information that is entirely false.
"3. We want to show our support for the character of our coach, Jose Mourinho, to whom we owe the greatest respect.
"4. Finally, we wish to convey to the members and fans of Real Madrid our unalterable conviction that only through the unity of everyone at Real Madrid will we overcome all the challenges that we face each season.
"Hala Madrid (Go Madrid)."
Club president Perez was unequivocal in his criticism of the article in his lunchtime press conference held in the directors' box at the Bernabeu.
"It's totally false that there was un ultimatum from the players," Perez said.
"I have not spoken to Mourinho. I don't normally come out to deny reports, but this was too important. This crossed an ethical line.
"I have only come here to deny a news story that has destabilised our club and the players.
"I understand some people want the coach or president out, but what has been published is a lie.
"We (the board) are the only ones that will decide the future of our club."