Clarke missed Saturday's loss at Southend United with a calf problem but the Irish striker is hopeful of being involved when the Bantams entertain Northampton at the Northern Commercials Stadium.
Along with Clarke though, McCall admits that the Bantams have some other injury doubts within their squad ahead of the visit of the Cobblers.
With this in mind, the City chief has revealed that he will be leaving it as late as possible before naming his starting XI for Tuesday night's fixture.
McCall said: "It is far better today (Monday) for Billy.
"We've had it scanned and there is no tear in there.
"We believe it was just a coagulation of the blood which has now loosened off a bit.
"He is desperate to be involved but we won't take any risks with him either.
"He has a better chance of playing on Tuesday night than he did at the weekend. If he keeps improving the way he has been doing he'll give himself a chance.
"We also have a couple of other bumps and bruises around the squad at the moment so we haven't named the team as of yet.
"We will leave it until when the lads meet up in the dressing room before the game.
"We will take everything into account but we will probably make at least a couple of changes to freshen things up with it being Saturday-Tuesday-Saturday (games) this week."
After being sidelined recently with a troublesome thigh problem, Tony McMahon returned to full training at Apperley Bridge this Monday.
The plan is now to have the right back step up his recovery with some match minutes in Wednesday's Central League (reserves) Cup game against Rotherham United.
McCall added: "Tony joined in with full training today (Monday).
"He won't be involved in the squad on Tuesday but we have a reserve game on Wednesday against Rotherham which he will play in.
"The aim is to get 45 minutes to an hour under his belt."