Varane has drawn the interest of Man United and Paris Saint-Germain this summer.
The France international’s current deal with Real Madrid is due to expire at the end of next season.
The 28-year-old will be available to sign on a free transfer next summer and he is expected to be available for €60 million (£51.5m).
Reacting to the development, Perez insisted that Varane is free to leave Santiago Bernabeu if he wants to, adding that Real Madrid are yet to receive an official offer for the defender.
“I read news in the newspapers [about Varane leaving], and I don’t know anything,” Perez told El Transistor.
“We have not spoken with him yet, he is at the European Championship. He still has one year left on his contract. And we have not received any offers for Varane.
“He is a gentleman, if he wants to stay, he will stay and, if not, he will leave.”
Varane is currently at the Euro 2020 with France national team.
He will hope to lead his country to victory when they face Switzerland in the round of 16 on Monday.
