The consensus for Gordon Strachan to be named the next Scotland manager is building after Alex McLeish effectively ruled himself out of the running.

Strachan is the firm favourite to succeed Craig Levein, who was sacked on Monday evening. McLeish has also been mooted as a candidate but the 53-year-old, who managed Scotland in 2007, played down the notion of a return to the post.

"I left the national team to take up club football, I felt I was missing the day-to-day stuff," he said. McLeish resigned the post and became Birmingham City manager, despite some notable victories, including against France in Paris. "I'm still of that mind. I wouldn't like to be unfair to the Scotland fans in terms of coming back to the job. A lot of people would maybe think I was a hypocrite. 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."

On Strachan, his former team-mate at Aberdeen, McLeish added: "Gordon Strachan is a pretty good candidate to me. He's had success at club level with Celtic."

Gary Caldwell, the Wigan Athletic and Scotland centre-back, also played under Strachan at Celtic. "I think so, he's a passionate manager and a very passionate Scot," said Caldwell of the likelihood of Strachan succeeding in international management.

"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. I'm sure he is a guy who will come with a real passion and do well for Scotland."

Strachan has yet to break his silence but it is understood he would be keen on it. His latest successor as Celtic manager, Neil Lennon, has also spoken on behalf of Strachan but claimed Scotland's players must take responsibility for recent woes. "I'm biased but I'd go for Gordon," Lennon said of the former Coventry City and Southampton manager. "I don't know if he'd thank me for that. I don't know what his thinking is and I know he's enjoying his media work. But for me he's an outstanding candidate for the job.

"The players need to have a look at themselves as well. They need to leave egos at the door and put the whole focus on Scotland for the two weeks or however long they are away from the clubs. I'm not sure all of them have done that looking at performances and attitude. The next manager has to be really, really disciplined and set down his rules and the players have to adhere to them."

The Scottish Football Association has said it will wait until after next week's friendly in Luxembourg before starting the process of replacing Levein. Billy Stark, previously the Scotland Under-21 coach, will name a squad for that encounter on Wednesday but some experienced names – including Scott Brown and Allan McGregor – are expected to sit the game out.