But he has no desire at this stage of his career to take over from George Burley, who was sacked earlier this week.
McLeish said: "I said after the World Cup exit that the Scottish FA (Football Association) should back George but you knew he would be scrutinised in every game and, if he didn't get results in the first couple, he would be under pressure again.
"Unfortunately, results never went for George. Circumstances were difficult but no one has sympathy for that side of things, like injuries and not being able to pick your best players.
"It can cost managers their jobs but in Scotland they have got to look forward."
McLeish continued: "Is it a job I would want to return to now? No. I've got a fantastic challenge here at Birmingham.
"I am really enjoying it and building a team and infrastructure which hopefully can keep us in the Premier League for a few seasons to come.
"I loved my time with Scotland, a fantastic journey which was part of my education in football and it is a phenomenal honour to manage your country.
"But I am very happy at Birmingham and will be even happier if we get to January showing the same performance levels of the last few weeks."
Aberdeen manager Mark McGhee branded the post "a rotten job" following Burley's departure, but McLeish disagrees.
"The Scotland job is not a poisoned chalice," he said. "It would be a great honour for someone to take the job and anyone with any ambition would say they can make it better.
"I'm sure the SFA will still target managers who are in jobs and I am sure they will be targeting Scots.
"If a foreign coach came in, everyone would want to back him but it is more likely to be a Scot."