There is a 10-day window, until May 23rd, for the submission of candidacies, Madrid said in a statement.
Among the requirements to be a candidate are having been a club member for 20 years and providing a guarantee of 187 million euros, equivalent to 15 per cent of the club's annual budget, which must be backed by personal assets.
Perez, who was re-elected unopposed in January 2025 for a four-year term, announced at a press conference on Tuesday that he will run again.
Spanish media reports Enrique Riquelme, the president of the water and energy group Cox, is considering entering the race.
In a letter published by several outlets in Spain, the renewable energy businessman asked Perez for more time to potentially prepare a candidacy.
"When I ran in the 2000 elections, I didn’t ask for more time; I ran, and I won," said Perez in an interview on television channel La Sexta on Wednesday.
If multiple candidates stand, the electoral board will announce the date and place of the elections in due course.
If no one else comes forward, Perez, 79, would retain his post, as happened in the 2013, 2017, 2021 and 2025 elections.
The Spanish businessman was first elected as Madrid president in 2000, overseeing the club's Galactico era, and resigned in 2006.
Since Perez returned in 2009, Madrid have won five Spanish league titles and a remarkable six European cups, among other silverware.