Having left Scotland for a second stint at Ibrox in January 2007, Smith said that he could not see himself going back to the national team although his future at Rangers remains unclear, with his contract due to expire in January.
Craig Levein has been installed as the favourite by several bookmakers and the Dundee United boss is thought to be open to an approach from the Scottish Football Association, an organisation he has clashed with several times.
Souness, who lost out to Burley in the interview process last time, has already told BBC Scotland he has no interest in returning to any job in football management.
Meanwhile, Burnley manager Owen Coyle has ruled himself out of consideration for the post.
"I'm the Burnley manager and I'm loving everything I'm doing at the football club," he said before offering Scottish football fans some words of hope.
"You want someone who can deliver success. There's no reason, with the young group of players that is coming through and the right man in charge to add that magic ingredient, why Scotland can't go on to qualify for major championships," added Coyle.
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