Los Blancos have long been linked with Mbappe and their desire to lure the World Cup winner to the Spanish capital is no secret.
Their hopes of bringing Mbappe to the club appeared to take a blow after Mauricio Pochettino claimed the attacker would "100 per cent" be at Parc des Princes next season, but Perez has revived speculation after witnessing his club clinch the league title.
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What did Perez say about Mbappe transfer?
He added: "When we plan next year's squad, we'll see."
Blancos boss Carlo Ancelotti was also quizzed on the possibility of signing the PSG star and gave a cryptic response, telling beIN Sports: "Mbappe to Real Madrid? With this club, with this president, the future is already written."
However, when asked if that was meant as a confirmation that the deal was done, the Italian coach replied: "I didn't say that."
Will Mbappe transfer to Real Madrid?
Mbappe remains Real Madrid's number one transfer target, but PSG have sought to convince him to stay in France by tabling a bumper €50 million-a-year contract.
Such a deal would make the 23-year-old the highest-paid player at the club, surpassing the likes of Neymar and Lionel Messi on the finance front.
Mbappe's future is complicated somewhat by questions over image rights, with PSG understood to be happy to facilitate the France star's desire for 100 per cent control. Real Madrid, however, are only willing to agree to a 50-50 arrangement.
PSG sporting director Leonardo made light of Madrid's pursuit of Mbappe in April, joking that the Spanish giants seemed over-confident of their chances of landing the talented striker.
"In Madrid, they’ve been convinced for three years that Kylian Mbappe would end up at Real Madrid," he told Sky Sport Italia. "Maybe they’re a little too sure about that?"