Strachan told ITV: "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.
"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 began his managerial career at Coventry City in 1996 and has since had spells in charge of Southampton, Celtic and Middlesbrough.