"What we are definitely going to do is bring in two or three top players to complete the squad," Perez said in an Internet chat organised by television station Antena 3.
The construction magnate oversaw an unprecedented spending spree of 250 million euros on his return to the presidency last year but Real failed to win any silverware and coach Manuel Pellegrini was sacked and replaced by Portuguese Mourinho last month.
Real have been linked in the Spanish media with several players including Inter Milan's Brazil right back Maicon, Sevilla's Spain winger Jesus Navas and Benfica's Argentina midfielder Angel Di Maria.
Asked about Maicon, who played in Mourinho's Champions League-winning Inter side last month, Perez said: "There is no rush but Maicon is one of the top players in his position."
On Navas and Di Maria, he added: "They are two players who I also like very much but I think it's still too early and we will work over the summer to bring in those players who will complete the magnificent squad we already have".
Perez also said the club were tracking Girondins Bordeaux's France midfielder Yoann Gourcuff.
"Some have even said he is the new (Zinedine) Zidane," Perez said, referring to the former France and Real playmaker.
"He (Gourcuff) is a player we have followed in the same way as others who we think will be the top players of tomorrow."
Asked whether he would ever try to prise Lionel Messi away from arch rivals Barcelona, Perez took the chance to compare the Argentina forward with Real's record signing Cristiano Ronaldo.
"Messi is the second-best player in the world after Ronaldo and it would not be a good thing to have both in the same team," he said. "That way there is more competition."
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