Davies has been sidelined since early October after undergoing surgery to rectify a knee problem.
The former Middlesbrough defender has returned to training this week with the rest of his City team-mates but Parkinson still isn't sure exactly when the 29 year-old will be back in first-team contention.
Parkinson said: “It’s too early for me to say about any particular games (for a return). We’ll have to see how that goes. “He is not too far away with the way he has progressed. His knee feels really strong, which is a good sign.
“He needs to get some really good football training under his belt. Once he’s had this full week, we will assess him after the weekend.
“Seeing Andrew Davies back will be a huge boost for everybody. The lads know he is a very good player – as good as any centre back at this level.
"We don't want to rush him back just to see him get another injury. It will definitely be a big boost to the squad when he comes back into contention for match selection."
"His knee feels good and he is definitely getting closer but we need to make sure we don't rush him. He has been away from football for over three months now and we need to get his body back playing football again.