Following Derby County's decision to recall Mason Bennett at the start of the week, Parkinson has been keeping himself busy over the last few days trying to bring in a new recruit to increase his options for the visit of the Blades to the Coral Windows Stadium.
Despite his best efforts though, the City chief admits he has yet to secure a deal for any player at the moment, with no guarantees in place that anything will be done in time for the Sheffield United game either.
Parkinson said: "We are trying (to bring a loan player in).
"We've made a few phone calls this week but nothing has come up so far.
"The problem we have is that we need someone who is match fit now and ready to go.
"We can't afford to waste three or four weeks getting a player up to speed."
With Gary Liddle suspended and James Hanson continuing to be hampered by a thigh problem, Parkinson's options do look a bit limited going into Saturday's Sheffield United game.
To make matters worse, some other members of his squad have been dealing with knocks during this week.
As City look to bounce back from last Sunday's defeat Barnsley, Parkinson is pleased to see, however, that no-one has been using the bumps as an excuse to shy away from the fight.
Parkinson added: "We have a few niggles in the squad but everyone has been out on the training ground this week.
"Not one player has taken the easy option and stayed in the treatment room.
"They are showing that they want to be selected, and that is great to see for myself and the rest of the staff.
"Our options are limited but those available have shown a desire this week to be in that starting eleven come Saturday evening."