Davies missed last Saturday's defeat at Oldham Athletic after limping out of the draw at Bristol City four days earlier due to the recurrence of an old calf problem.
The 29 year-old received an injection towards the back end of last week and returned to training today (Thursday) to give himself a chance of playing against Doncaster this weekend.
Davies' presence back in City's ranks would be a welcome boost to Parkinson ahead of the Doncaster fixture, especially with fellow centre half Rory McArdle suspended because of his Oldham red card.
Parkinson said: "He's (Andrew Davies) a lot better now.
"He has returned to training today (Thursday) so we'll have a look at him tomorrow (Friday) to see how he is ahead of the weekend.
"The injection he had has worked for him in the past and it seems to have worked again this time.
"We are hopeful he will be fine and that the problem has cleared up."
While Davies might be in contention for the Doncaster derby though, Parkinson has revealed that midfielder Gary Liddle will almost certainly miss out after picking up a hamstring injury in training this week.
Parkinson added: "Unfortunately Lids (Gary Liddle) has got a tight hamstring.
"There is a slight strain in there so I would suggest that this weekend might come too soon for him, especially with the heavy grounds that are around at the moment.
"Everyone else is fine though and raring to go. We want to have a real go at Doncaster on Saturday and play 'front-foot' football."
In other news, Parkinson has confirmed that former Wolves striker Sylvan Ebanks-Blake is currently training with the club.
Parkinson revealed: "He is training with us at the moment. We want to see where he is in terms of his fitness and how he fits in with the rest of the squad."