Former Celtic boss Strachan was asked about the Scotland job while working as a pundit on ITV's Champions League programme on Tuesday night.
"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," he said.
"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."
The former Celtic boss, 55, is the strong favourite to take over from Craig 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 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.
Meanwhile, Glasgow-born Coyle has been out of work since he was sacked as Bolton manager in October but has been touted as a candidate to replace Levein. Coyle would welcome an approach from the Scotland Football Association 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."