The former Celtic manager is the leading contender to replace Craig Levein, who was sacked on Monday after a poor run of results that have left Scotland's hopes of qualifying for the 2014 FIFA World Cup™ in Brazil hanging by a thread.
Strachan was asked about the possibility of becoming Scotland manager while working as a pundit for ITV on Tuesday. He 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 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," the 55-year-old added.
"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 enjoyed success during a four-year spell at Celtic from 2005 but has been out of management since leaving English club Middlesbrough in October 2010.