Gordon Strachan and Owen Coyle have both expressed cautious interest in replacing Craig Levein.
The former Celtic boss, 55, is strong favourite to take over from Levein who was sacked by the Scottish Football Association on Monday following a poor start to the 2014 World Cup qualifying campaign in which Scotland have taken only two points from four games.
Strachan said: "It's quite simple really, it would be an honour to be asked to be the manager of your own national side, it's terrific.
"I could say 'yes, it would be great' or 'no, it's not for me' but it would also be arrogant of me to answer that if nobody has asked you and presume that someone will ask.
"Until you've been asked a question about a job, any job, then you really don't know how you'd go about it that's for sure. I wouldn't have the arrogance to think that someone is going to knock on my door."
Strachan spent four largely successful years at Parkhead from 2005 but has been out of management since leaving Middlesbrough in October, 2010.
The former Scotland international, who played for Aberdeen, Manchester United and Leeds among others, will be at Parkhead tonight to watch Celtic's Champions League Group G match against Barcelona.
Coyle has admitted he would welcome an approach to discuss the possibility of taking over as Scotland boss.
Glasgow-born Coyle has been out of work since he was sacked as Bolton manager in October and revealed he had already turned down clubs in England since leaving the Reebok Stadium.
"I'm always open to hearing what someone has to say. It's a great job, that's for sure," Coyle told BBC Radio Scotland.
"It's a fantastic job for whoever's lucky enough to be asked to lead Scotland. I've already turned down a couple of approaches down here, but I've listened to what people have had to say.
"And, for me, the next thing has to be the right fit in terms of matching the same ambition as I have. There's no doubt there's a good squad of players there."
Coyle won a single cap for the Republic of Ireland as a player but spent most of his playing days in Scotland while making his name as a manager with St Johnstone.
And while the 46-year-old would like to fill Levein's shoes in Scotland's top job he admitted his sympathy for the outgoing boss.
"My first thoughts are with Craig, as I get on very well with Craig," he said.
"I think we all understand how that works in football, and I wish him well for his speedy return to the game.
"I think Scotland are very fortunate that there's many fantastic candidates capable of doing that job."
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