Parlour missed the draw against Wigan last week with a hip injury, while Schwarzer (shoulder) and Morrison (ankle) both picked up injuries in the game.
Boro boss Steve McClaren may have to gamble with one or two of the five players returning from injury.
Jimmy Floyd Hasselbaink, Szilard Nemeth, Gaizka Mendieta, Stuart Parnaby and Chris Riggott all returned to full training at the beginning of the week, but they are all lacking match fitness.