With James Meredith, Reece Burke and Lee Evans all away on international duty currently, Parkinson will have to make changes to his starting line up for the visit of Crewe to the Coral Windows Stadium.
Parkinson is expected to go with Nathan Clarke and Greg Leigh at centre half and left back respectively, whilst Christopher Routis could also come into contention after recently returning to training following a calf complaint.
While Clarke and Leigh haven't featured too heavily for City so far in the league this season, the pair both put in impressive displays against Barnsley in the Johnstone's Paint Trophy last month and Parkinson has no qualms about calling upon them again if required.
Parkinson said: "It is a shame to not have three players to call upon but it at least gives players who have been working hard in the background a chance to stake a claim.
"Nathan Clarke and Greg Leigh have been terrific in training - their attitude has been fantastic. We also have Christopher Routis back in training now so we do have some players hungry to be given the opportunity to get in that team and stay in there.
"Nathan has captained a team at this level to a Play-Off Final two years ago, Chris Routis has been great for us in both midfield and defence, and Greg played over 40 games for Crewe last season.
"These are not inexperienced players but it is up to them now to show us that they should be in the team every week."
As one of the club's three players away on international duty at the moment, City left back Meredith made his full debut for Australia in their World Cup qualifier against Kyrgyzstan in Canberra on Thursday.
Featuring from the start, Meredith played the whole game as the Socceroos ran out 3-0 winners. Australia now move on to play Bangladesh in Dhaka next Tuesday.
Parkinson added: "I'm really pleased for James and for his family. I'm sure they will all be very proud of him.
"It is great for us as well as a club to have a full international in the squad. It is long overdue and, like with Rory McArdle really, I feel James should be getting in his national squad on a regular basis.
"I'm sure he is feeling top of the world at the moment.
"James has worked hard to get into his national side and Rory has to keep doing the same himself and hopefully he will get that recognition soon as well."