Scotland parted company with Craig Levein on Monday after a disappointing start to their World Cup qualification campaign which has seen them plummet to the bottom of Group A after collecting two points from four games.
However, McLeish, who managed the Hampden Park group in 2007, believes there is enough quality in the nation's ranks to see them rise again - and back above Uzbekistan, Haiti and Libya in the Fifa rankings - especially if Gordon Strachan takes charge.
"I don't believe it is an impossible job as there are some decent players there who just haven't shown they are capable of yet," said McLeish, who left the Aston Villa dugout over the summer.
"There is a fair sprinkling of Premier League players in there, when in the past 10 years we haven't had any Premier League players, and these guys need to raise the bar a little bit.
"I think Gordon Strachan has the presence and experience - if not the height! - to take the job; respect of the players is key and Gordon, who has played for and managed top clubs, could get the guys to buy into his methods - ones that at Celtic earned him three Scottish Premier League titles."
On Levein's sacking, McLeish added: "I thought the SFA would make their decision pretty quickly so the longer it went on and the way they spoke about Craig's work at the grass-roots level and the infrastructure he has put in place, the more I thought he was going to stay in the job.
"However, the Tartan Army wanted results and we never got away to the flyer at home and then we had two defeats away to Wales and Belgium - and that was the nail in the coffin.
"When you are in the hot-seat and you have new players, are playing young kids, or have injuries, you want a bit of understanding - but that all goes out of the window when you don't get results."
Scotland's international malaise, Rangers' implosion and the news that Edinburgh outfit Hearts could fold if they do not raise £450,000 within the next seven days, has painted a gloomy picture of football north of the border.
But McLeish reckons Celtic's victory over Barcelona in the Champions League on Wednesday night, which has put the Hoops in with a real chance of making the knockout stages, will go a long way to restoring some national pride.
"Celtic have done the nation proud in their two games with Barcelona, (the narrow defeat away and the win at home)," said the ex-Rangers boss. "It was a rearguard action but they were really organised, even though Barca's magic picked the locks at times.
"To beat Barcelona is up there in anybody's book and the whole of Europe will be jealous of their result and this has given the Scottish game a real big boost.
"And it was one it needed, with us losing our national team manager, Scotland on a bit of a downer in the qualification group for the World Cup in Brazil, and the crisis at Hearts, where they are looking at the punters to save the club."