The St Andrew's chief will face his old Derby pal after Carsley replaced the sacked Marinus Dijkhuizen as Brentford boss until the end of the season on Monday
Blues travel to Griffin Park in the Sky Bet Championship on Tuesday having lost 2-0 at home to Rotherham on Saturday, with the Millers also having parted company with boss Steve Evans
Head coach Dijkhuizen lasted just nine games after replacing Mark Warburton in the summer, despite Warburton guiding Brentford to the play-offs last season
Brentford, 19th in the table, parted company with Warburton wanting a change in structure and Rowett feels the traditional manager is being phased out
He said: "A lot more clubs are doing it, there are going to be less and less Championship managers who can solely pick the team
I think it's creeping down a European route where there's a head coach and more influence from other people within the club
"I spoke to Nigel Clough about it the other day and I said we're becoming a little unique
I'm not saying it's a bad thing but it's becoming quite unique to be a manager with no outside influence
"It could be positive but I'm sure some managers would say they would prefer to pick the team and pick the way they play and not have anyone to answer to because it makes it simple
Every club does it their way and football moves in cycles, 20 years ago the manager would have been the definitive voice, things are changing."
Birmingham are ninth in the table and would move into the top six with a win on Tuesday but despite playing with Carsley, Rowett admitted he will not know what his friend will do at Griffin Park
He added: "Not really, I know he didn't like peas in his omelette, he used to have it every Saturday - chicken omelette
That's all I know about Lee's philosophy because there's so many other variables
"
Source : PA
Source: PA