Paris St Germain boss Carlo Ancelotti has emerged as the favourite to succeed the departed Jose Mourinho, who was named Chelsea manager on Monday after three years in the Bernabeu hotseat, although the French champions have made it clear they expect the Italian to honour the final year of his contract.
Zidane, meanwhile, has remained with the club in various roles since hanging up his boots in 2006, and may now fancy a crack at becoming a coach, according to Perez.
"From next week with Zidane, we will see," the president told Spanish radio station Onda Cero's 'Al Primer Toque' programme last night.
"We have not talked to any coach. We are studying what is the best option. A few years ago Zidane would not have considered being on the bench, but now he has the idea of taking on the title of coach."
Perez claimed in an interview on with Spanish television station Telecinco on Tuesday that Zidane fulfilled all the requirements, saying: "(Zidane) could be the coach. He has the qualifications and is a madridista."
The 66-year-old insisted the Primera Division outfit had not yet spoken to any candidates, though, and were in no hurry to seal a deal.
"In the coming days, we will look at the coaching staff and decide what we want for next season," he told Spanish television programme Los desayunos de TVE this morning.
"We will not rush, because the important thing is not to do it tomorrow but to do it well.
"Ancelotti is an option, but no one has spoken to him, no one has offered anything. When we have thought about what is best, what we need, we will make the appropriate movement."
Perez, just starting the second term of his second spell as president after being re-elected unopposed last week, continued on 'Al Primer Toque': "Ancelotti is a great person, he was a great player, now a coach - one capable of winning big leagues - and can manage high-level players.
"(At the moment) he is at PSG (so) today it is not an option.
"(But) everything in life is possible.
"PSG must do what they think is best. If the possibility of Ancelotti exists, we will analyse it."