The ex-Aston Villa boss tips his former Old Firm rival for the role and distances himself from a return to international management in the near future after Craig Levein's sacking
McLeish won seven of his 10 matches during a brief spell as Scotland boss in 2007 but resigned in order to take over at Birmingham City.
However, he has distanced himself from a return after stating that he has unfinished business at club level, instead naming Strachan as his preferred successor to the recently sacked Craig Levein.
"Gordon looks a pretty good choice," McLeish told talkSPORT.
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"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."
The 53-year-old has been out of work since being sacked by Villa in the summer but says that he is waiting for the right offer to come along.
"There's nothing really pending," he added. "I had to have a break after Aston Villa and now I've got itchy feet again."