The 28-year-old sustained an ankle injury in the Minstermen's 4-0 Johnstone's Paint Trophy defeat to Coventry on Tuesday and confirmed via Twitter that he was on crutches.
However, after going for scans on Wednesday, Mills is optimistic Walker could play against the Bantams.
"There is no fracture so that is good news," he told Press Association Sport.
"We will take each day as it comes, there is bruising around the bone so it depends on the pain level.
"He might be Ok for Saturday, we will have to wait and see."