Parkinson's men should head into the fixture in fairly confident mood after Tuesday's impressive 3-1 victory over the previously-unbeaten Crawley Town.
Opponents Peterborough tasted defeat last time out at the hands of Sheffield United but they have won their other two League 1 fixtures so far this season.
After giving striking duo Aaron Mclean and Mason Bennett a half each at Crawley's Checkatrade.com Stadium in midweek, Parkinson must now decide which player he wants to start with alongside James Hanson for the Peterborough game.
Parkinson also faces a choice whether to stick with Filipe Morais or revert back to Mark Yeates in City's advance midfield role after the Portuguese former Stevenage attacker got the nod against Crawley.
Billy Clarke is edging closer to full fitness following a recent hamstring problem but this Saturday's fixture will probably come too soon for the Irish striker.
Looking ahead to the game, Parkinson said: "We have had a good start but we know that the table means nothing at this stage of the season - we are certainly not getting carried away.
"We are pleased with our start but we now know we must put in the same sort of effort and commitment we showed against Crawley on Tuesday into this Saturday's game if we want to get a positive result from the match.
"Peterborough play a high-energy brand of football and they were unlucky to lose out to Sheffield United during the week. We will have to match them physically.
"This week has been all about giving the players the chance to recover between Tuesday's match and this Saturday and to get that energy back in their legs.
"I am sure the supporters will be behind the team as always during the game and making that home advantage count."