Morris has been sidelined since the middle of September with damage to his knee ligaments but the 24 year-old has been received injections in the problem area to try and finally resolve the issue.
City thought Morris was close to getting back in contention when he travelled with the squad to Millwall at the end of last month but the former Fleetwood Town man was still feeling some discomfort with the injury.
The Bantams are hopeful it is second time lucky for Morris now, however, with the aim being to try and get him back in the picture for at least one of City's two games next week.
Parkinson said: "He had another jab this week but that was just a scheduled one. It was just part of the course of injections he's been having.
"We don't want to get too carried away because we've been here before but he is feeling a lot better now.
"Let's hope he's back in contention come next week."