Tony Pulis was believed to be the early-front runner for the vacancy at Pride Park following Nigel Clough's sacking after Saturday's defeat to arch-rivals Nottingham Forest.
Clough, who was the longest-serving manager in the Championship, was relieved of his duties following a 1-0 defeat at the City Ground.
Darren Wassall has been placed in temporary charge of first-team affairs after four of Clough's coaching staff were placed on gardening leave.
The Derby board has told Andy Garner, Gary Crosby, Johnny Metgod and Martin Taylor to stay away from the club.
Clough's brother Simon, who was appointed chief scout at the beginning of 2011, has also been placed on gardening leave.
And academy boss Wassall - a former County player who was a team-mate of Clough at Forest - will lead the team into Tuesday's home game against Ipswich.
Lee Glover and Pat Lyons will assist Wassall as speculation continues over who will replace Clough on a permanent basis.
Sky Bet have made McClaren a firm 1/10 favourite, with former Stoke manager Pulis drifting to 5/2.
A Derby statement read: "The search for a successor to Clough continues, and further announcements will be made in due course."