The Spanish giants are still to name a successor for Jose Mourinho, but the Paris Saint-Germain boss is their number one target.
Former France coach Laurent Blanc revealed on Sunday he was due to hold talks with the French champions, which could pave the way for Ancelotti's move to the Bernabeu.
Perez said in an interview with Spanish paper 20minutos: "As of today nothing is signed. It could be tomorrow that PSG announces an agreement which allows him to move to Madrid.
"Hopefully everything goes well. My coach is Ancelotti."
Asked what the appointment depended on, he said: "That PSG reach an agreement with Ancelotti and announce their new coach, Blanc."
He added: "PSG president (Nasser Al-Khelaifi) is an open-minded man. He was a professional tennis player and is very young. He is a modern president."
Perez also re-emphasised his belief that Cristiano Ronaldo would sign a new contract at Real Madrid, despite reports linking him with a return to Manchester United.
The forward is under contract until 2015, but took to Twitter recently to claim "all the news about my renewal with Real Madrid are false".
Perez said: "Cristiano made these statements because there was some information in the media which did not match reality.
"Soon we will clarify this issue. I have no doubt that Cristiano is going to retire at Real Madrid. I am convinced that he will renew."
He added: "It (renewing with Ronaldo) is our most important activity, around whom we can build the Madrid of the future."
Perez also claimed he was confident of sealing a deal for Malaga midfielder Isco.
The 21-year-old has been heavily linked with a move to the Bernabeu this summer with some reports in Spain suggesting a deal has already been agreed.
"He wants to be a Real Madrid player and Madrid want him," he said.
Madrid defender Sergio Ramos believes the Spain Under-21 international would be major asset for the club.
"Isco is a great player and anything Madrid does to strengthen with the squad with players of the highest level is always something to be happy about," he told Spanish radio station 'Onda Cero'.