The reports said Calderon, who has denied any wrongdoing, was pushed into resigning by several members of the Real management board and would be replaced by Vicente Boluda, one of the club's vice presidents.
Asked about the reports, which did not identify any sources, a Real Madrid spokesman said the club had no immediate comment.
Calderon, 57, has been under pressure since Marca reported this week that unauthorised persons gained access to the club's assembly on December 7 and their presence had helped swing votes on key issues in favour of the management.
"None of us participated either directly or indirectly in these acts," he said. "We did not do anything. We are victims."
Perez resigned in 2006 after his six-year experiment in assembling a "galactico" super team collapsed as the club headed for a third successive season without a major trophy, their worst run in more than 50 years.
Calderon has been unable to make good on a pledge to bring Arsenal midfielder Cesc Fabregas and AC Milan's Brazilian playmaker Kaka to the club and his attempt to lure Manchester United winger Cristiano Ronaldo also ended in failure.
