Centre-half Cooper was forced out of Friday night's home defeat to Sheffield United with a dead leg and has not recovered.
Midfielder Phillips received his fifth yellow card of the season against the Blades and sits out a one-game ban, while defender Gaetano Berardi completes a three-match suspension.
Defender Cameron Borthwick-Jackson (ankle) remains doubtful and striker Caleb Ekuban has returned to full training after a foot injury which has kept him out since August.
The trip to Elland Road looks like it will come too soon for Johnny Russell.
The forward missed Derby's 2-1 victory at Norwich on Saturday due to a groin strain and the visit of Reading at the weekend seems a more likely return date.
Striker Matej Vydra had a calf problem ahead of the Canaries clash and also during the match but the injury was nothing to do with him being substituted at half-time at Carrow Road, according to Rams boss Gary Rowett.
Meanwhile, defender Jason Shackell sustained a calf injury while playing for the Under-23 side last week.