The 18-year-old is believed to have attracted interest from numerous clubs, including Arsenal and Liverpool, but Madrid have been the early favourites to land his signature.
When asked about the speculation, Perez told esRadio: "He is a very good player, it reminds me of last year of when they said that we would sign [Paul] Pogba.
"The summer is very long, [Zinedine] Zidane has had a close relationship with him for several years, but very few players play at Real Madrid at the age of 18 He should have patience, the coach has it in his mind. It's not worth saying if we are going to bring in players who could be on the bench."
Mbappe scored 26 goals in all competitions for Monaco last season.