Dolan suffered the injury in the warm-up before last Saturday's home loss to Yeovil Town at the Coral Windows Stadium.
With the emergency loan window now open again for Football League clubs, Parkinson hasn't completely ruled out dipping into the loan market to strengthen his midfield in Dolan's absence.
Parkinson admits that any potential moves don't look likely at present, however, given the fact that he feels City have cover within the squad already for this area.
James Meredith played in midfield during City's recent Johnstone's Paint Trophy tie at Oldham Athletic, while Filipe Morais, who returned to training this Thursday after a slight thigh strain, can also play a role in that area of the pitch.
Speaking about the state of City's squad going into this Saturday's home fixture with Swindon Town, Parkinson said: "We picked up a few things off the back of last week's Oldham and Yeovil games but Filipe Morais is back and training with us again, which is a bonus for us.
"Alan Sheehan, equally, has trained this week after having a slight problem with his thigh last week. He put himself up for selection for the Yeovil game but we had a fitness test on him before the match just to be sure.
"He looks a lot better this week.
"Matty Dolan is the one negative, however.
"He should be out for two to three weeks with his hip problem. There isn't much we can do about that - we just have to be patient and wait for him to improve.
"I wouldn't definitely rule anything out (in terms of loans) given Matty's injury but we do have cover in that area. James Meredith can play there, Filipe Morais can play there, plus we also have young Sam Wright from our apprentices who was on the bench last weekend.
"James missed our photo-shoot on Tuesday with a bit of illness but he was back training today (Thursday).
"Any player coming in would need to be better than what we have here already and be fit enough to drop straight into contention for selection."
Following a busy opening to the new campaign, this week has been City's first clear week without a game since the season started against Coventry City early last month.
After nine games in four weeks at the beginning of the season, Parkinson feels his squad will have benefited from the slight break in their schedule over the last few days.
Parkinson added: "I felt we needed it (the break).
"If you look at players like Stephen Darby, who have played every minute of every game so far, he played at Oldham last Tuesday having had a bit of a sickness bug and then played the Saturday against Yeovil.
"Hindsight is a wonderful thing but I probably should have just left Stephen out of the Oldham match but he is a player, as fans will know, who wants to play all the time.
"For players like him, this week has been a good opportunity to have some time at home and also to have some time out on the training pitch. I feel the squad as a whole will benefit from this."