The influential Republic of Ireland centre-back sustained the injury while away on international duty a fortnight ago forcing him to sit out last weekends 2-2 draw with Fulham.
Now 'King Kenny' is struggling to shake-off the injury in time for Blues' game at Elland Road this weekend.
"The groin's not too bad and there has been an improvement," Cunningham told the clubs official website on Thursday morning.
"Sunday came round too quickly for me, but hopefully I will be able to step things up over the next couple of days."
