Manager Neil Lennon will look to offer Daniel Majstorovic a new contract if the Swede continues his current form at the heart of the Celtic defence.
"I think Majstorovic has been a really consistent performer in the last five or six games and that has given us an air of solidity," said Lennon.
"I will speak to him in January and we will see how he is feeling.
"He's enjoying it here and, if he keeps playing the way he is, it will be difficult not to offer him something."
The 34-year-old arrived at Celtic Park from AEK Athens in August 2010 and has not always been a fans' favourite, with some erratic performances.
Majstorovic's current deal ends at the end of the season and the Sweden international has helped Celtic concede just two goals in their last six Scottish Premier League outings.
"He has shown tremendous character," added Lennon.
"He was a wee bit up and down but he has found his form now.
"He had a family bereavement not so long ago and I think that might have knocked him out of kilter a bit, which is totally understandable but we always knew that he could come back to the player that we want.
"He is experienced, assured, strong, dominant in the air and is dealing with things earlier and you can see the players getting a lift."