Calderon, who has held the post since 2006, has been under pressure to go since Marca newspaper published allegations earlier this week of irregularities at the club's general assembly last month.
No one was available for comment from the club but a news conference has been called for 1700GMT at the Bernabeu, when Calderon will speak to the media, a statement said on the club's website.
The 57-year-old, who has denied any wrongdoing, was close to resigning on Thursday night under pressure from several members of the Real management board, reports said.
It is predicted that Vicente Boluda, one of the club's vice presidents, will take the helm until new elections can be called.
The allegations in Marca this week said unauthorised persons had 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.
At a news conference on Wednesday, Calderon said two Real officials involved in organising the assembly had resigned and he would probably not stand for re-election when his four-year mandate ended in 2010.
He ruled out stepping down immediately and insisted neither he nor any other member of the management board were involved in any irregularities.
