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Perez said he did not know who the next coach would be after Jose Mourinho - whose contract has been terminated "by mutual agreement" - but he was clear about Zidane being the new sporting director.
"We did not know who will be the coach. Until next week we will not talk about that subject. What we do know is that Zidane will be the leader of the new sporting project," he said.
Zidane, 40, played for Real between 2001 and 2006, then returned to the club two years ago as a special adviser to Perez, only to get on badly with Mourinho.
Perez declined to talk about the two leading candidates for the coaching post, Carlo Ancelotti of French champions Paris Saint-Germain and Jupp Heynckes of European and German champions Bayern Munich.
However, when asked about Juergen Klopp of Champions League finalists Borussia Dortmund, he said: "Klopp "I like him, he is a good coach. However, the players of Dortmund are younger than ours, and so I am not sure that his style would be effective here."
Real has not paid any compensation to Mourinho and his assistants.
"The contract was terminated by mutual agreement, it was the best for everyone," Perez said.
He denied that Mourinho had been given excessive power within the club, saying: "All the coaches here have had the same power. The difference is that each one has his own particular personality."
Perez also denied that there was a dressing-room revolt against the controversial Portuguese coach.
"The players only spoke well to me about Mourinho, they told me he was the best. I don't think there was a revolt against him," he said.
He also denied Mourinho had damaged Real's public image, with his disputes against certain players, referees, media and fans.
On Mourinho's feud with club captain Iker Casillas, Perez said: "For me, Casillas is the best goalkeeper in the world. However, the coach decided to drop him for technical reasons. The club cannot interfere in a technical decision.
"I think that several team-mates and journalists tried to help Casillas but actually ended up doing him harm."
He was also quick to deny that Real's season had been a failure, despite no trophies being obtained.
Cristiano Ronaldo will be given a salary increase in order to keep him happy at the club, Perez said.
"We are going to do whatever is possible to make him happy," he said.
"He is the best player in the world, without a doubt. I would like him to be the best paid player in the world, and construct our team around him."
Real also want to keep veteran midfield anchorman Xabi Alonso.
"He is one of the best that we have, as player and a person," Perez said.
"To find a replacement for him in the future will be a problem, but we would still to enjoy him being here for another year or so."
He admitted that he had tried to prevent Neymar from signing for Barcelona, but had to accept defeat when it was clear that the Brazilian youngster was determined to join the Catalans instead of Real - despite Perez offering him a higher salary.
Perez would also love to sign world player of the year Lionel Messi from Barcelona.
"If he was available then of course I would like to sign him," he said.
When asked about young forward Isco of Malaga, he replied: "We are going to improve the team by buying the best players and Isco is a great player, though I do not know if he is what we need most of all."
Young right-back Dani Carvajal, who was sold to Bayer Leverkusen a year ago, will be brought back to the club.
"I think he will return, he is one of ours. He will be back here soon," Perez said.
Zidane and the new coach will meanwhile decide whether Brazilian veteran Kaka stays.
"It is true that he has not given us what we wanted, in sporting terms, but he was unlucky with an injury. However, he has been useful to us with regards to our publicity contracts," he said.
Perez was asked whether he had altered the club's statutes in order to continue indefinitely as president. Candidates now have to have been club members for at least 20 years and also be able to cover 15 per cent of the club's budget with their own personal assets.
So far, no other potential candidates have been able to fulfil these conditions. If nobody manages to do so by the June 3 deadline then Perez will automatically continue for what will be his fourth four-year term.
"If no other candidates come forward it will be for other reasons, not because I have changed the statutes," he said.
