Zidane was appointed Real manager in January 2016 and in his short time has already win the Primera Division, the Champions League twice, a UEFA Super Cup and a FIFA Club World Cup trophy.
His two-and-a half year deal is fast running out, and Perez says he will tie the World Cup winner down to a new deal as soon as possible.
Perez told esRadio: “Sure he is safe and the first thing we are going to do after he comes back from holiday is renew him.
“No one knows the club and the dressing room better than him. It is an advantage that he has over the rest and that has made him succeed for 17 months.
“Many times he has said that he does not know if he will continue so that they [the press] do not ask him about the future of the players.
“But I would have continued with him even if we had not won.”
Perez has, meanwhile, also talked up the talents of James Rodriguez, who may be on the verge of a Real exit.
He added: “He is one of the best players in the world.
“He is at Madrid… we have to match the interests of the players with ours, but prevailing those of Madrid.”