The Blues boss had been in charge of the Scotland national side before taking on the managers role at St Andrews almost two years ago and his name has been touted in the press as a possible replacement for George Burley, who was sacked as Scotland coach earlier this week.
"I said after the World Cup exit that the Scottish 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," McLeish has said.
"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.
"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."