Bantams defender Rory McArdle will undergo a scan on his shoulder injury this Monday afternoon.
McArdle was forced off in the closing stages of Saturday's goalless draw at Bury after the defender dislocated his left shoulder following an awkward fall.
City will now have to wait for the results of the scan to determine how serious McArdle's injury is and how long he is expected to be out for.
Parkinson said: "Rory will be having a scan today (Monday).
"The shoulder was obviously dislocated on Saturday so we are waiting to see the extent of the injury.
"He has been in this morning with his arm in a sling. There is clearly pain and discomfort there for Rory, we'll just have to see what damage has been done when the shoulder came out."
Despite initial fears that Steven Davies could be sidelined for a significant spell after injuring his knee at Blackpool, the striker trained with the rest of the squad this Monday as he continues on his road to recovery.
Parkinson added: "Steven has trained most of the session this morning.
"That is certainly great news for ourselves and Steven because we were fearing the worst when the injury first happened."
After being sidelined since September with a broken leg, Paul Anderson is scheduled to play some part in City's Final Third Development League reserve fixture at Burton this Wednesday.
Filipe Morais, who has been out of action since damaging his knee back in pre-season, should be in line to play in the club's reserve match at home to Wigan Athletic the Tuesday after.
Parkinson continued: "All being well, Paul will play in the reserves at Burton on Wednesday.
"We are hopeful that Filipe can play in our reserve game the week after (against Wigan Athletic).
"For me, if they get through those games, we can begin to consider them up for contention once again. If that is the case, it will be a huge boost for us."