Valdano, sports director of Real Madrid under Perez during the "Galactico years" earlier in the decade, said three potential candidates were being considered.
"We are working in private on a plan, without haste, and you will all find out what that is in due course," Valdano told reporters.
"There are three options. I'm not going to say who is first second or third, but there is a coherence that links them all, and they all adhere to a particular style."
"The people under consideration are currently working and nothing has been agreed. It will become clearer from Monday when we will be able to speak more freely," he added.
Spanish media have linked Perez with interest in Arsenal's Arsene Wenger, Inter Milan's Jose Mourinho and Villarreal's Manuel Pellegrini among others.
The registration period for presidential candidates closes on May 31 and club members "socios" get to vote on June 14. If only one candidate stands he will be appointed president on June 1.
