Portuguese Mourinho, who spent three seasons at Real from 2010, was dismissed by Chelsea on Thursday after a shocking run of results left the west London club one point above the Premier League relegation zone.
Benitez has been under pressure in recent weeks as Real's La Liga campaign faltered and they were expelled from the King's Cup for fielding an ineligible player, and he is widely expected to be discarded if Real's results do not rapidly improve.
"Nobody can predict the future but as things stand no," Perez told Cadena Ser radio's "El Larguero" (the crossbar) show when asked if Mourinho would be coming back.
"I have good memories of him," added the big-spending construction magnate.
"He raised the level of competitiveness. We were Champions League semi-finalists three times and we didn't make the final due to ill luck."
Mourinho's time at Real was generally considered a disappointment, with only one La Liga title and one King's Cup to his name among the three main competitions.
His stint in the Spanish capital was marked by a number of ugly clashes with arch rivals Barcelona, where the Portuguese worked as an assistant coach in the late 1990s, while he remains popular among a hard core of Real supporters.
Perez insisted Benitez, who has been regularly whistled by the home fans at the Bernabeu in recent months, was capable of turning Real's fortunes around and dismissed reports the coach has a poor relationship with the players.
He also said Real had not been talking to any other prospective candidates, with Germany coach Joachim Loew also said to be in the running, and that it was too early to promote B team coach Zinedine Zidane.
"We are only thinking about Rafa Benitez," Perez said.
"I say that he is the coach and that he was the right person to solve a problem we have had since January.
"I have a lot of respect for Zidane. Many people still thank me for bringing him in.
"I feel an adoration for him and he will be a great Real coach but not just yet. We have to give Benitez time."
Real host Rayo Vallecano in La Liga on Sunday.
(Reporting by Iain Rogers; Editing by John O'Brien)
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