After his first appearance in claret and amber at Sheffield United a week and a half ago, Mclean made his home debut for the Bantams this Tuesday during the goalless draw with Preston North End.
The powerful forward was twice denied a maiden City goal by smart saves from Preston 'keeper Declan Rudd before he was replaced by Oliver McBurnie with 18 minutes of normal time to play.
For Mclean, the Preston outing was only his sixth start of the season at first team level after spending the first part of the campaign with Hull City and on loan at Birmingham City.
Parkinson doesn't believe City fans have seen the best of Mclean just yet but he knows that the striker is putting in all the effort required to get him firing on all cylinders as soon as possible.
Parkinson said: "With Aaron, he is someone who we are going to have to work our way up with to get him to his full sharpness.
"Having said that, he has still got himself on the end of two good chances.
"It was great movement in the penalty box to get a powerful header on goal in the first half and he has gambled well off (James) Hanson's flick for the one in the second half. Aaron's tried to put it under the 'keeper but he's made a good save.
"We have to expect not too much of him too soon but he is a great lad and he is training well. He is working really hard to get as sharp as possible."
Mclean's first half headed opportunity came thanks to a searching cross from City debutant Adam Reach.
On loan from Middlesbrough, Reach looked a lively figure on his first Bradford outing, especially in the second half, and Parkinson was encouraged by his display.
Parkinson added: "It took a while for us to get the ball out to him on the left hand side but I thought he was excellent.
"He got better and better as the game when on, and it was a big effort from him because he hadn't played since 1 January in terms of first team action.
"With the sending off, we had to play Adam slightly narrow for the remainder of the game in a three-man midfield but he is a confident boy and he has great athleticism."