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.

The Dons twice led in the first half, through David Fitzpatrick's 20-yard strike and Tom Elliott's volley.
But Compton levelled on both occasions, running through to slide home and curling in a free-kick from out wide.
And the winger sealed his treble from the penalty spot after substitute Kevin Dawson was fouled by Callum Kennedy.
The home side drop to 10th in the table after seeing their four-game winning run come to an end, while the Glovers are three points ahead of Dagenham & Redbridge, whose match was postponed.
AFC Wimbledon manager Neal Ardley told BBC Radio London:
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"You concede three goals at home, that's not good enough.
"I knew this would be tough and I drummed it into the players. That's the sort of game I expected.
"We struggled at times and we had too many players who probably didn't perform to the levels they have performed at. We're giving away really, really poor goals.
"We ran out of ideas trying to chase the game in the last 20 minutes."

The Reds had failed to score more than once in their previous 10 League Two games, but were dominant against Warren Feeney's side.
County striker Scott Boden opened the scoring at the wrong end when his header beat Joe Day after 36 minutes.
Shamir Fenelon then headed home eight minutes after the break, before Newport's Medy Elito was sent off with five minutes left for two yellow cards.
"It was disappointing, I don't think we got going from the first whistle, we couldn't get into a rhythm and our passing was poor," Newport manager Feeney told BBC Radio Wales.
"We have to put it to bed and move on to the next game, we are still in a fantastic position to avoid relegation and that is still my aim.
"You have ups and downs in a season and this was a down, the worst performance since I have been the manager. No-one likes to get beaten."
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.
[NEXT_CONCEPT]
Jack Compton hit a hat-trick to earn a shock comeback win at AFC Wimbledon and take Yeovil Town three points clear of the League Two relegation zone.
[NEXT_CONCEPT]
Crawley completed a double over Newport County with a comfortable 2-0 victory.