Nearly three weeks since the defeat to Belgium left Scotland bottom of their World Cup qualifying group with two points, the Scottish Football Association announced on Monday that Craig Levein was no longer in charge.
Though McLeish has been linked with a return to the post he held in 2007, famously winning away at France, he has backed the current favourite Gordon Strachan to take the job, as he wants to return to club management having left Aston Villa at the end of last season.
McLeish and Strachan were team-mates together with Aberdeen and Scotland but became rivals when their managerial reigns at Rangers and Celtic overlapped.
"Gordon looks a pretty good choice," McLeish told talkSPORT. "I don't want to say I don't want the Scotland job but I feel I've still got some time left in club football.
"I left the national team to take up club football. I felt I was missing the day-to-day stuff. I wouldn't like to be unfair to Scotland fans in terms of coming back to the job and being a hypocrite.
"There's nothing really pending, I had to have a break after Aston Villa and now I've got itchy feet again."
Strachan, who won three league titles with Celtic, is currently out of work having left Middlesbrough after a difficult spell in 2010.
Meanwhile, former Scotland striker Joe Jordan is pleased to be mentioned as a possible contender.
Jordan, who served as first-team coach at Tottenham under Harry Redknapp, has welcomed reports linking him with the Scotland job.
"I know there will be a lot of names, a lot of speculation," Jordan, who has managed Hearts, Stoke and Bristol City, told BBC Radio 5 Live. "I am Scottish, I'm a proud Scotsman and a person that wants to work. And, for my name to be mentioned, yes, it's nice to be linked with the national job."
As well as Jordan and bookmakers' favourite Gordon Strachan, Kenny Dalglish has also been linked with the post, although former Scotland forward John Robertson believes whoever takes charge faces a tough challenge.
"It's a hard job. The Tartan Army demand a lot, the press demand a lot. The players are certainly talented but it's getting the results, you have to get results as a manager," Robertson said.
"I don't see the benefit of changing mid-campaign because if one of the big guns that they're talking about - Strachan, Dalglish, Joe Jordan - come in and don't do well for the rest of the campaign they could be under pressure before the end of this campaign finishes."