The City skipper is to undergo pain killing injections ahead of the game at Bramall Lane to see if that can cure his ankle injury.
"Stephen is getting better, although there is one tiny area at the front of his ankle that is causing him discomfort," manager Craig Levein told the clubs official website.
"A specialist is going to put some sort of injection into it to see if that will take away the pain."
Elsewhere, striker David Connolly has recovered from a groin injury and will be in the squad for the game on saturday.
"David will be involved on Saturday," Levein added.