Lopetegui is under intense pressure at the Santiagao Bernabeu just four months after taking over from former Madrid boss, Zinedine Zidane.
Madrid suffered a 1-0 shock defeat to Alaves on Saturday evening in the La Liga to make it four matches without a win in all competitions.
The Los Blancos also lost to Sevilla and CSKA Moscow and played a draw with Atletico Madrid.
Spanish outlet, Onda Cero reports that Perez held meeting with the club’s board members to discuss the potential sacking of Lopetegui on Sunday.
The report claimed that after the meeting, Perez was willing to give Lopetegui more time to turn things around for Madrid.
Lopetegui had stated that he was aware of the possibility of being sacked following his side’s poor performances this campaign.
“Every football manager is aware of the possibility of being sacked.
“But I don’t think about it. We are still in October.
“We apparently have a negative dynamic.
“But we could be three points away from the top in the worst case scenario,” he had said.