The hearing follows legal action launched by Barcelona on June 12th over comments made by Perez in May accusing the Catalan club of manoeuvring to obtain favourable treatment from referees.
Barcelona said its action was intended to force Perez to retract statements it described as knowingly false, defamatory and damaging to the club's image and reputation.
It warned that if the conciliation process failed, it would file a criminal complaint.
The dispute centres on comments Perez made at a May 12th press conference concerning the so-called Negreira case.
Spanish courts are investigating payments said to be up to seven million euros made over almost two decades by Barcelona to companies linked to Jose Maria Enriquez Negreira, a former vice-president of Spain's refereeing committee, to determine whether they were intended to obtain a competitive advantage.
Barcelona denies wrongdoing and says the payments were for reports on referees and a court dismissed bribery charges against Barcelona in 2024.
Perez described the affair as "the most serious case of corruption in football", adding: "We could never have imagined Barcelona giving money to the head of the referees."
He also claimed Real Madrid had been denied league titles, saying: "I've won seven leagues. I could have won twice as many. The others were stolen from me."