Parkinson is hopeful that striker Andy Gray could make up part of his plans for the Bramall Lane fixture after missing the last four games with a dead leg.
Gray picked up the problem during City's away fixture at Peterborough United last month.
The injury damaged a nerve in his upper leg which meant a longer spell on the sidelines than originally expected for the experienced forward. Gray is back building up his training now, however, and could be back in the reckoning soon.
Along with monitoring the progress of Gray, Parkinson will need to assess the fitness of both Ricky Ravenhill and Nathan Doyle ahead of the weekend.
The central midfield duo of Ravenhill (ankle ligaments) and Doyle (groin/hip) are definite doubts for this Saturday due to recent injuries. Doyle has missed City's two previous games after picking up a problem in the recent Swindon Town home game, while Ravenhill limped off during the first half of the Bristol City fixture.
Young forward Oliver McBurnie, who played 77 minutes last Saturday, has a slight hamstring problem.
James Meredith had an operation on Tuesday after breaking a bone in his right foot last week. The injury is likely to keep him on the sidelines for around 4 to 6 weeks.
Fellow defender Andrew Davies, who has been sidelined since October with a knee problem, is still targeting a return in early February.