The ex-England boss, 54, was due to meet the Rams hierarchy on Friday.
But the meeting has been brought forward following Derby's failure to reach the Championship play-offs and growing unrest about McClaren's link to the manager's job at Newcastle.
McClaren is understood to be resigned to leaving the club.
Only last week Rush said the season review should not be too "draconian".
But McClaren's refusal to completely rule out a move to Newcastle when the rumours first began upset some of the board members, including director Mel Morris who is set to take over from chairman Andy Appleby.
And although McClaren did reject the chance to take over as Magpies manager in May, and said he was "100% committed to Derby", there is a feeling that his refusal to quash the rumours in the first place played a part in the club's poor end-of-season run.
The Rams were leading the Championship in late February but won just two of their final 13 games and missed out on the play-offs on the final day of the campaign when they lost 3-0 at home to Reading.
Morris, who was last year appointed to the club's board, is set to be confirmed as the club's new chairman in the coming weeks.
Derby head coach Steve McClaren is to hold talks with chief executive Sam Rush on Thursday amid speculation he may be sacked, BBC Derby Sport reports.