Having missed City's Easter fixtures due to international duty, midfield duo Lee Evans and Josh Cullen are back available to Parkinson for Scunthorpe's visit to the Coral Windows Stadium.
Cullen did suffer a slight thigh problem while away with the Republic of Ireland Under 21s but he is expected to be fine for the weekend.
Both Evans and Cullen will face a battle for a starting place, however, after Tom Thorpe and Billy Knott came into the side and helped City to back-to-back wins over Easter.
Out on the flanks, left winger Kyel Reid is doubtful for the Scunthorpe game after struggling with a chest infection this week.
If Reid is deemed unfit, Parkinson could turn to either Paul Anderson, Filipe Morais, Mark Marshall or Josh Morris to replace him.
Parkinson also has options in central defence for Saturday, with Reece Burke back in contention after being rested at Crewe Alexandra on Easter Monday. Rory McArdle could also be in the Saturday's match-day squad after returning to training following a recent shoulder problem.
Nathan Clarke and Christopher Routis were the pair at the heart of City's back four against Crewe last time out.
Should Parkinson wish to change things in attack, the City chief has the likes of Steven Davies, Wes Thomas and James Hanson waiting in the wings just behind current strike partners Billy Clarke and Jamie Proctor.
For opponents Scunthorpe, Iron boss Graham Alexander has confirmed that midfielders Jim O'Brien (groin) and Stephen Dawson (knee) will need to be assessed pre-match to see if they have any chance of being involved at the weekend.
Both O'Brien and Dawson missed Monday's impressive 6-0 win over Swindon Town at Glanford Park because of their injuries.
Even if the pair are passed fit to play though, Alexander could well be tempted to stick with the same starting XI that began the rout over Swindon last time out.
That would mean another start for Hakeeb Adelakun after the young winger scored once and set up two other goals against a beleaguered Swindon side. Adelakun scored an injury time equaliser for Scunthorpe against City at the Coral Windows Stadium last season.
David Mirfin and Neal Bishop picked up bumps during the mammoth Swindon win but both are expected to be fine to feature against the Bantams.
Defender Scott Wiseman is a long-term absentee for the Iron. Wiseman, who has been capped at full international level for Gibraltar, has a knee injury.