Northern Ireland international Taylor played a major role in helping Blues gain promotion to the Premier League last term.
But McLeish has preferred on-loan Manchester City player Joe Hart for the opening three league games.
McLeish confirmed Taylor will play in Tuesday night's Carling Cup clash at Southampton and believes he has a long term future at the club.
The former Scotland boss said: "Maik is a good pro. He is not happy being dropped because he was number one last year.
"When I came he was number three here. I wanted Maik's experience back in the side and he was brilliant last season.
"Leaving him out this season was a tough decision for me. But we have chosen to go with Joe Hart from the beginning and it is Joe's jersey to lose.
"What I do know is I have got a top class keeper ready to come in. Maik will play at Southampton. Both of them have different attributes but they are two good goalkeepers."
McLeish added: "Can Hart learn from Taylor? Definitely. Maik is a superbly honed athlete at the age of 38 and I am sure he will sign a longer contract when this one finishes.
"We gave him a new contract last season and there is no reason why he can't go on. You have seen the top keepers stay on a long time as long as they keep themselves in trim.
"The likes of Brad Friedel at Aston Villa and David James at Portsmouth are still playing at top level."
McLeish is poised to give a first start to record signing, striker Christian Benitez, after he has appeared as a substitute in the opening three games.
He said: "Benitez is still an unknown quantity, coming in from South America, but he is looking a real prospect.
"The crowd were excited by his introduction against Stoke on Saturday. That is another 30 minutes under his belt and he will play at Southampton and is probably going to be ready to start the game."
McLeish will check on the fitness of full-back Gregory Vignal (hip) and striker Cameron Jerome (ankle) who both missed the goalless draw with Tony Pulis' side.