Riquelme has already outlined ambitious plans for the club, including attempts to sign Manchester City stars Erling Haaland and Rodri.
He has also promised to bring club legend Raul back to the Santiago Bernabeu as sporting director.
"We know that Jurgen Klopp has publicly stated that he has no intention of returning to the dugout in the short term, and that he has turned down numerous offers,” a statement from Riquelme's office read.
"That is precisely why we believe the challenge of Real Madrid is different. Because there are great clubs, but there is only one Real Madrid. There is only one institution capable of uniting tradition and future, values and ambition, passion and excellence.
"For that reason, if the members grant me their trust this Sunday, on Monday June 8, Raul Gonzalez Blanco (Real Madrid's sporting director) will contact Jurgen Klopp to convey to him personally our sporting project and our wish for him to be the one to lead, from the bench, our new era at Real Madrid."
Meanwhile, Perez is reportedly pursuing his own high-profile targets, including Jose Mourinho, Denzel Dumfries and Ibrahima Konate.