Speaking to El Español, Pérez, who is seeking a seventh presidential term on Sunday, said: "We will have names before Sunday, don't worry. People don't doubt me — they know me.
"I have always generated excitement in the 23 years I have been president. Those who know me know that the best players will be at Real Madrid and that some Champions Leagues will come.
"Thursday I will announce the first major signing."
He dismissed Riquelme's claim of having secured Rodri — the Manchester City and Spain midfielder whom the challenger pledged to sign if elected — as entirely unverified.
"He says he has Rodri closed, but obviously he doesn't. I am getting calls from agents telling me Riquelme speaks to players and says: 'Don't say no.' I don't believe a word from him."
Pérez also addressed Riquelme's central campaign argument — that the club faces financial distress and requires urgent capital — attacking both the substance and the source.
"If the other candidacy says we are in debt and we are the richest club in the world, how are the rest of the Spanish clubs doing then? It is a lie that a valuation is needed because of a credit to renovate the stadium. The credit carries an interest rate below 3% and there is €1bn still to pay. The stadium pays for itself annually from the income it already generates."
On his Bernabéu Infinito project — allowing supporters to watch matches in immersive virtual environments — he responded to Riquelme's criticism of the cost of Apple Vision Pro headsets.
"Don't worry. This will be a global phenomenon and the price will come down. We are in the middle of a technological revolution in football."
Pérez confirmed that head coach José Mourinho's appointment will be announced "shortly."