Davies limped off in the first half of City's home fixture with Stevenage at the weekend, sparking concerns the influential defender could be set for a spell on the sidelines.
The centre half is set for hospital tests this Tuesday on a suspected calf problem but Parkinson believes the injury is not too serious.
Parkinson explained: "It is a not a muscle injury. It seems to be same nerve issue he had at times with his back last season.
"The problem is with the nerve when his calf tightens up.
"We should know more this week but it something we hope we can resolve.
"It can come and go for Andrew. He had it last year when it affected him for the Chesterfield and Rotherham United matches.
"We thought he'd got over it but it is something we have managed in the past and we are confident we can sort out now. It shouldn't be a major issue."