The Bantams striker moved to London Road on loan last year and cannot play against his parent club under the terms of that transfer.
Mclean could, though, have been free to sit alongside Robertson after the pair were asked to take charge of first-team affairs following the recent sacking of Darren Ferguson.
Parkinson said: “Obviously, we are in something of an unprecedented situation. I did hear that Aaron had said he wouldn’t be in the dugout, which is a sensible thing to do.
“I wasn’t too concerned about it, to be honest. But I think the right decision has been made.
“Aaron has been given a chance that will provide plenty of experience. It will not do him any harm, either. He is at a club where he has had a lot of success and will be keen to help out in any way he can.”
Mclean tweeted earlier this week that he would not be sitting in the home dugout as he did not want to disrespect the Bantams.
For City, the target today is a return to winning ways after a frustrating week that saw Parkinson’s men pegged back in a 1-1 draw at home to Walsall before slipping to defeat in midweek at Swindon Town.
The Bantams manager was left irate by a failure to award his side a penalty at the County Ground and he believes the Football League should look at adopting a similar system to the top flight in that referees should work with the same linesmen every week.
He added: “It is not fair on the referees that the first time they meet an assistant is on the day of a match. That can’t be right and it helps no-one.”