Madrid's members will be invited to vote on the proposal that would require a change to its statutes at an extraordinary general meeting in the near future, Perez said at the club's annual meeting.
He also said the current ownership-by-members model would remain intact and that being a member would now have "a real and tangible value."
"If someone is willing to invest significant amounts of money for a symbolic stake, this is the greatest demonstration of Real Madrid's value," Perez told the club's members in an hour-long speech repeatedly interrupted by applause.
"This investor - or investors - must respect our values, contribute to the growth of the club and help us to protect our assets from external attacks," he said.
Like Spanish rivals FC Barcelona, Athletic Club and Osasuna, Real have a membership model. Some 2,000 of the club's members are selected as delegates to the annual meeting, where they can elect the club's president, review annual accounts and vote to change their statutes.
An initiative to open the ownership to outside investors would follow a deal by US fund Apollo this month to become the majority shareholder in Real's rival Atletico Madrid, the latest venture into soccer by private equity firms attracted by the sport's stable and predictable revenue streams.
Real are the only club in world football to have recorded revenues of more than 1 billion euros, according to Deloitte. Revenue for the 2024/2025 season grew to 1.19 billion euros, while net revenue after tax increased by 56% to 24.3 million euros, Perez said on Sunday.
At $6.75 billion, the club has the highest value in global football, according to business magazine Forbes.
But Perez has said the membership model holds them back, especially when competing in the transfer market against rival European clubs such as Paris St Germain, Manchester City or Chelsea, owned by private equity, billionaires or oil-rich states.
Real Madrid have led the push to create a European Super League, with Perez arguing it would be a way for the club to stay competitive.
At last year's assembly, Perez broached the idea of holding a referendum on the reorganisation of the club's ownership structure that would "protect us from threats we face" - while stressing the club would continue to be owned by its members.
Under Real Madrid's bylaws, the club is required to hold an extraordinary meeting to change the statutes and their structure. Real already have deals in place with US private equity firms.
In 2022, they reached a deal with Sixth Street in which they would receive 360 million euros in exchange for handing over rights to develop and operate new businesses over 20 years at the Santiago Bernabeu stadium.
Real Madrid take on Elche on Sunday evening - follow the game with Flashscore.
