After being troubled by a back problem in recent weeks, Hanson was ordered to rest up towards the end of last week and over the weekend, meaning the giant forward missed Saturday's victory at Leyton Orient.
Hanson's progress will be checked once more in the build up to Tuesday's date with the Sky Blues but Parkinson has confirmed that both Adam Drury (knee) and Nathan Doyle (groin) will definitely miss the match.
Drury had to be substituted in the first half at Orient after picking up the injury while Doyle has missed the last two games because of his own issue.
Parkinson is hopeful, however, that at least one of the pair might be fit for this Saturday's home match with Oldham Athletic. Andy Gray is still sidelined with shingles.
The City chief said: "Hans (James Hanson) has had five days of complete rest and is feeling a bit better this (Monday) morning.
"I will be having a chat with Matt (Barrass, Head Physio), Nick (Allamby, Head of Sports Science and Fitness) and James himself before the game to see where we go now.
"Tuesday will unfortunately come too soon for Adam. We don't think it is a serious knee injury but it will keep him out of the game.
"We will assess him again later in the week. Often with knee ligament injuries, they need a couple of days to settle down before you can get a clear indication of when a player will be fit again.
"(Nathan) Doyley is out as well but getting better."