Mclean missed all of City's pre-season friendlies due to a calf problem but he has featured as a sub in both of the Bantams' games so far this season, scoring the winner at Morecambe on Tuesday in the process.
Parkinson knows that Mclean still has a fair way to go before he can be considered to be fully match-fit but he feels that the striker has the right attitude in place to get him there as soon as possible.
Parkinson said: "There is still a bit to go before Aaron is fully fit but he is getting there.
"He has trained well this week and he has a real appetite to get back sharp. That is really encouraging to see.
"I think the supporters could see that desire in Aaron when he came on against Morecambe on Tuesday.
"While he got the match-winner, his all-round determination and application was what really stood out for all to see.
"In terms of his fitness, the other lads are still a long way ahead of him after the work he missed out on in pre-season.
"He has missed out on those 45 minutes, 60 minutes and 90 minutes you normally get as a player in pre-season friendlies so we do still have to be careful with him.
"Equally though, he is champing at the bit to get involved and play his part."
Along with a returning Mclean, Parkinson now has the presence of pacey forward Mason Bennett to add to City's attacking arsenal.
The Derby County loanee, who will wear 28 during his time at the Coral Windows Stadium, took part in his first training session this Thursday after penning a half-season loan deal earlier this week.
Parkinson added: "Mason looked great (today).
"He is a powerful and quick boy and he is enthusiastic about the opportunity to come and play for Bradford City.
"I am sure he will show that hunger and enthusiasm to our supporters when he gets the opportunity."
Having signed with City until the start of January, Bennett will be looking to be involved when City travel to Walsall in League 1 this Saturday.
Another player also aiming to feature against the Saddlers is Gary Liddle after the midfielder missed the Morecambe match to attend the birth of his first child.
Alan Sheehan could miss the trip to the Banks's Stadium, however, after returning to Ireland to deal with the death of a close relative.
Parkinson added: "Gary Liddle is fortunately back in contention for us after his partner gave birth to their first child this week.
"We would like to add our congratulations to Gary and Leanne on the birth of their new daughter.
"Unfortunately for Alan (Sheehan) he has had a family bereavement and he wasn't with us today.
"Our thoughts and prayers are with Alan and his family back in Ireland."