Zidane has led Los Blancos to back-to-back Champions League titles, in addition to wresting the La Liga crown away from Barcelona last season.
The Madrid giants have only won three of their last eight matches in all competitions, however, and are currently eight points off the pace being set by Barcelona in Spain's top flight.
While it has been suggested that Zidane's job was under threat, Perez has lavished praise on the Frenchman, insisting that he is "the best leader this team could possibly have".
"Zidane is the best leader this team could possibly have," Marca quotes Perez as saying.
"What he has achieved is unique, he is a wonderful coach who is now an even greater icon here and he has already won the Spanish and European Super Cups this season."
Madrid were held to a goalless draw by Athletic Bilbao in La Liga at the weekend.