The Spanish giants are still searching for a successor to Jose Mourinho after the Portuguese’s three-year reign in the Spanish capital came to an end last week.
But PSG have so far refused to allow Ancelotti to speak with Madrid as the Italian has a year remaining on his contract in France.
“He is a coach that currently has a contract with another club,” was quoted as saying to newspaper Marca on Monday.
“If you ask me is Ancelotti a coach that is liked within the club, I would say that everyone knows that on two occasions he was on the brink of becoming the coach of Real Madrid.
“We are talking about a coach that has won two European Cups, he has managed important squads, he is used to the pressure and he knows how to manage it.
“It would be like a curse for him to miss out on becoming Real Madrid coach for a third time.”
Perez has been famed throughout his two spells as president of Real for his tendency to buy some of the world football’s biggest stars.
But he also hinted at a change of attitude this close season by saying that competition for places does not always breed the best results.
Strikers Karim Benzema and Gonzalo Higuain both struggled to find their best form consistently last season and Perez believes neither being an automatic first choice could have affected their confidence.
“My opinion is that at Madrid, two top players in the same position could produce the opposite effect and this year we have seen this in one position,” he added.
Madrid’s only signing so far this close season has been 21-year-old Dani Carvajal on a buy-back option from Bayer Leverkusen.
Perez said he would like to see more of the club’s academy products graduate to the senior side.
“If it were up to me, there are three players that ought to be in the first team: Jese (Rodriguez), (Alvaro) Morata and Nacho,” he said.