The 1998 World Cup winner shocked the football world by stepping down as Los Blancos head coach just days after winning the Champions League for the third year in a row.
Speculation has been rife over Zidane's reasons for abruptly leaving the role, with some pundits claiming that the Frenchman simply wanted to leave on a high.
According to The Sun, however, the 45-year-old had told Perez that he wanted to sign Chelsea forward Hazard and Manchester United goalkeeper De Gea, only for the president to disagree with the idea.
The report adds that the debate went back and forth and ended with Zidane telling Perez: "I am done. You take care of the team."
Zidane was contracted to Real until 2020.