Director of football Gordon Smith feared the centre-half would be out for six weeks, but McCoist is more optimistic about the player's recovery.
McCoist told rangers.co.uk: "It's a big disappointment for Kyle that he's out for a bit longer, but I had a good chat with him last night after his operation and he's upbeat.
"He was obviously in a bit of discomfort and pain, but he still managed to ask me if there was any possibility we could put the Celtic game back.
"I thought that was wonderful and it sums up big Kyle. He doesn't want to miss any training or any games."