Perez became president of Real Madrid in 2000 and started off his stint with the huge signings of former world record transfer Zinedine Zidane, David Beckham, Luis Ronaldo and Luis Figo, who all became known as the Galacticos.
The Spanish businessman eventually resigned in 2006, but is currently in his second stint as president following the election in 2009, with the club currently experiencing their best years in a long time.
And Perez claims that if Messi, who joined Barcelona's academy in 2001, was at his current level during his first spell as president, he would have tried bringing him to Madrid.
"If there had been a Messi in my first stage [as president], I would have gone after him," Perez told Cadena SER, as quoted on FourFourTwo. "He is a type of player like Zidane."
As for whether Messi playing for Los Blancos in today's age is a possibility, Perez says it would be very difficult given the circumstances of his career.
Along with this, no contracted player has directly moved from Barcelona to Madrid and vice-versa since Figo made his infamous move to the Bernabeu in 2000.
"In my first stage, possibly," Perez added. "He is now a Barca player. He has been there since he was a kid. It would be very difficult."
Interestingly, there is some concern on Messi's future at the Nou Camp as despite Barcelona announcing back in July that an agreement had been reached over a four-year renewal, the 30-year-old is yet to put pen to paper.
The Argentine scored 54 goals in 52 games in all competitions last season, but was left frustrated as Barcelona were not able to win more than the Copa del Rey.