Zinedine Zidane sensationally quit Madrid after landing an historic Champions League hat-trick.
The Frenchman called an unexpected press conference last Thursday afternoon to reveal that he was leaving after two-and-a-half years in charge.
Perez did not agree with Zidane, who was also happy with his No 1 Keylor Navas.
The 45-year-old, a club legend as player and manager, said he felt it was the right time to go.
The Sun has reported that last Wednesday night Zidane and Perez did not see eye to eye over who they should sign this summer.
Zidane was keen to sign Chelsea star Eden Hazard while Perez wanted to pursue their interest in Manchester United goalkeeper David de Gea.
Zidane is claimed to have said: ‘I am done. You take care of the team,’ following the exchange between the pair.
Former Arsenal manager Arsene Wenger, Tottenham boss Mauricio Pochettino and former Madrid midfielder Guti are the front-runners to take over at the Bernabeu.
Appearing alongside president Perez at the press conference last week, Zidane said: ‘I have taken the decision to not continue going into the next season. For me and for everybody, I think the moment to change has arrived. It was not an easy decision.