The 26 year-old's current City contract runs out at the end of this month but Parkinson wants to check on the former Charlton Athletic and West Ham United man's progress as he continues to recover from serious injury.
Reid spent the second half of last season on the sidelines after rupturing his cruciate knee ligament at Sheffield United back in January.
With the speedster expected to still be working his way back to full fitness by the time City return to training at the start of July, Parkinson fancies a closer look at the player before making a decision on his future.
Parkinson said: "Reidy is going to come back for pre-season training with us and we'll see how he is.
"There is not an immediate rush with him though. The most important thing is that he makes a full recovery. He is doing well with his rehab and you'd expect him to come back from this.
"We just want to see how he goes and then we'll sit down with him."