Defender Davies, who returned to first-team action in January after knee surgery had kept him sidelined for four months, was forced out of the weekend defeat to Stevenage with a calf problem. He is set for hospital tests on Tuesday.
"It's a not a muscle injury," Parkinson told the club's official website. "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."
Davies, 29, missed three months of Bradford's promotion-winning campaign last season and most of their Capital One Cup run before returning for the second half at Wembley in the 5-0 defeat to Swansea in the final.