The combative midfielder played an integral part in the resurrection of the Toffees' fortunes under the guidance of Moyes during which time the club has qualified for Europe three times in the past four seasons.
However, Carsley opted to quit Everton at the end of last season and joined hometown club Birmingham on a Bosman free transfer, where he will look to help them secure promotion back to the Premier League at the first attempt.
But, since his departure, the former Blackburn and Derby man has highlighted the great work performed by Moyes and feels Alex McLeish can do similar things at St Andrews.
He said on the club's website: "Moyes turned round Everton completely from being a club at the bottom of the league to a club in the Champions League. The job he's done there is fantastic.
"Alex reminds me a lot of him in the way he speaks. He's very single minded."