Reid and Oliver both picked up knocks during Saturday's match at Oxford United, while Jon McLaughlin may be taken out of the firing line after battling through the Kassam Stadium victory with a sore hip.
Parkinson said: "Jonny Mac (Jon McLaughlin) played with his side problem on Saturday and he needed a lot of anti-inflammatory tablets beforehand to enable him to get through the game.
"He is fine this morning but we will wait until tomorrow (Tuesday) morning to have a final look at him.
"Luke Oliver fell awkwardly on his shoulder in the same (Oxford) game so that is another one we need to monitor.
"Reidy (Kyel Reid) took a whack on his ankle towards the end on Saturday, something which resulted in him coming off. Again, it's nothing too serious, but he's another one we'll need to assess beforehand."
Despite the prospect of changing a winning side from Saturday coming into his thoughts, Parkinson firmly believes any alterations made for tomorrow night won't weaken his starting line up.
"We will select the team that we think is going to be the best possible one to give us a performance tomorrow," Parkinson added.
"Looking back at the Gillingham game at the start of the season, we had Fleetwood the following Tuesday and made changes for that one. I felt the fresh legs in that team was very beneficial in helping us to win that (Fleetwood) game.
"There are players who are really desperate to play and then there are players currently in the side who have worked really hard to earn their shirt.
"We have to just strike that right balance for tomorrow night."