The 55-year-old will be in Glasgow today to attend the Champions League match between Celtic, the team he managed from 2005 until 2009, and Barcelona.
This is a long-standing family visit, and Strachan has no plans to speak to anyone at the SFA about the managerial position which became vacant on Monday when Levein was removed from his post.
However, the man who played for Scotland 50 times, and who was interviewed for the manager's job in 2004 before Walter Smith was appointed, made it clear he would be honoured to be invited to lead the national side.
Strachan, who has concentrated on TV work since stepping down as Middlesbrough manager two years ago, is the bookies' favourite to be the next Scotland boss, and 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.
"But, it would also be arrogant of me to assume.
"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 no-one has asked you and presume that someone will ask you."
He added: "Until you've been asked the question, then you don't know how you would go about it. I wouldn't have the arrogance to think someone is going to knock on my door."