The Hoops goalkeeper is on the mend following a neck injury which has kept him out of the last three matches.
Manager Neil Lennon said: "He is progressing slowly but will not be available tomorrow. Sunday against Raith Rovers might be an opportunity but we don't want to rush him back."
Sammy Clingan is eligible for his Kilmarnock debut after signing an 18-month deal.
But the Northern Ireland international is short of match fitness and is unlikely to feature against the champions.
Killie boss Kenny Shiels says he will rest several experienced players and throw in some youth-team players.