Levein was sacked on Monday following a poor start to the World Cup qualifying campaign, which leaves the Scots bottom of their group without a win from four games.
Former Celtic and Middlesbrough boss Strachan has emerged as the bookmakers' favourite to fill the vacancy and has the backing of Scotland defender Gary Caldwell and former national team boss Alex McLeish.
"He's a passionate manager and a very passionate Scot," Caldwell said.
"I had three good years with him at Celtic and he achieved great things there.
"He's been out of management for a while and I'm sure he will be hungry.
"I think the national team job needs a passionate guy. It is not an easy job."