Jones missed Tuesday's victory at Colchester United after struggling with a virus during the Brentford game a few days earlier.
The influential midfielder took part in training this Friday but Parkinson is wary of throwing the 36 year-old back into the fray too soon if he is not completely 100% fit.
Parkinson said: "Gary took part in sections of training today (Friday) but we are still awaiting results from a couple of doctor's tests to see exactly how he is.
"Given Gary's efforts throughout the season and in recent weeks, it probably wasn't the worst thing in the world that he had a little break and missed the match on Tuesday.
"As I say, he was back doing part of training today but we're not sure yet whether he's quite ready to come back into the fold.
"We don't want to rush him back when we have other important games still to go between now and the end of the season."