Craig Levein was sacked on Monday after Scotland opened their World Cup qualifying campaign with just two points from a possible 12.
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"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,” Strachan told reporters.
"I could sit here and 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 won three Scottish Premier League titles with Celtic, as well as one Scottish Cup and two Scottish League Cups, but has been out of management since leaving Middlesbrough two years ago.