Reid limped off in the second period of City's home victory over Swindon Town last weekend but Parkinson has revealed that the winger has been able to train as normal this week.
Tom Thorpe is also back in contention for the fixture at the Greenhous Meadow after missing the Swindon game with a shoulder injury. The Rotherham United loanee returned to training this Thursday.
Parkinson said: "Kyel is fine. He had a slight cut on his ankle from last Saturday but he has trained all this week.
Tom is back in training today, we'll just see how he is tomorrow before we sort out our group to travel (to the game).
"Everyone else is fine."
After seeing City secure their fourth win in a row against Swindon last time out, Parkinson could be easily forgiven for sticking with the same starting XI for the Shrewsbury fixture.
With a whole hosts of established pros, including the likes of Filipe Morais, Paul Anderson, James Hanson, Steven Davies and Rory McArdle, all chomping at the bit to get back into the team though, Parkinson knows picking his side for Saturday won't be easy.
Parkinson added: "It is good to have those options.
"We have some very good players out of the team at the moment but we also have some excellent players in the team as well.
"They are being driven on by the competition we have within the squad at present."