Backed by an expected away following of 2,000 - 3,000 City fans, Parkinson's men travel to Bramall Lane at the weekend looking to do the 'double' over the Blades following their home victory over the South Yorkshire side back in August.
City have been hampered in recent weeks by a number of injuries throughout their squad but Parkinson believes the situation is now slowly getting better.
Kyel Reid is expected to shake off a minor calf problem picked up during last Saturday's draw with Bristol City. Former Blade Andy Gray could also make the journey south after returning to training following four games out with a dead leg.
Ricky Ravenhill (ankle) and Nathan Doyle (groin/hip) are still rated as doubtful, however, while Oliver McBurnie is expected to miss out because of a slight hamstring problem.
Raffaele De Vita remains sidelined after suffering a small set-back recently while trying to return from a thigh injury.
Parkinson said: "Things are slowly improving for us but it is still not ideal at the moment.
"Raffa (De Vita) tried to come back into training but had a bit of a set-back. We think that is just a bit of scar tissue hindering him at the moment.
"Doyley is getting closer and Ricky's injury doesn't seem too serious, but we'll have to wait and see if they make the weekend.
"Ollie McBurnie's hamstring is tight after last Saturday so it is doubtful he will be available for the weekend."
While left back James Meredith is expected to be sidelined for at least the next month following an operation on his broken right foot this Tuesday, fellow defender Andrew Davies is nearing a comeback after three months out with a knee problem.
Davies has been included in small parts of training this week and it is hoped he could be back by early February or even sooner.
Parkinson added: "We have Andrew Davies coming back for us. He joined in training with the footballs for the first time on Thursday and he is making progress. He looked fine when he joined in with us.
"He is looking stronger by the day.
"I don't think it'll be too long now before he's back. He is getting more confident with his knee almost every day. Like last season when Andrew had the same injury, it didn't take long before he could play again once he got to the final stages of his rehab.
"We will keep building him up every day - it will be a big boost when we can get him back in contention for selection."