Following the defeat to table-toppers Burton Albion last time out, Parkinson is looking for a response from his squad and is open to change when it comes to his starting line up.
Reece Burke is fully fit once again after a recent Achilles problem, James Meredith has shaken off the twisted ankle that was troubling him last week, while Lee Evans is back after serving out a three-match suspension for his red card at Port Vale last month.
Parkinson said: "We have James Meredith back, his ankle is fine after training this week, and Reece Burke is back in contention as well.
"Evo (Lee Evans) is also back now after suspension.
"All of the players we had doubts with going into the start of this week are now in contention for this Saturday.
"I don't think anyone could complain if they were left out after last weekend (vs Burton Albion).
"It is just a case of us looking at Peterborough, which we have done, and looking at who is performing well in training and then picking the team which we think will give us the best chance of a positive result."
Although they are both some way off a first team return just yet, Filipe Morais (knee) and Paul Anderson (broken leg) both continue to make progress at City's training ground after picking up serious injuries earlier this season.
Parkinson added: "Those two are doing very good. Filipe has been training with us for a few days this week.
"We have been careful with him. Two days in succession on a hard surface like astroturf is maybe a little bit too much for him at this stage, so we are still checking his progress and monitoring his training sessions but he is doing well.
"Paul is coming on well and continuing to work hard with the physios, and Billy Clarke is making progress as well."