Armstrong, capped 63 times, is the IFA’s elite player mentor and says the anthem issue has cropped up in recent conversations with prospective players from a nationalist background.
A number of Northern Ireland-born players such as James McClean, Dan Devine, Darron Gibson, Shane Duffy, Marc Wilson, Daniel Kearns and Paul George have declared for the Republic in recent times.
“It is an issue which is sensitive to a lot of nationalist kids,” he said.
Part of Armstrong’s brief in his IFA mentor role is to attempt to convince Northern Ireland-born players from the nationalist community not to switch their international allegiance.
“It [the anthem] was an issue that was brought up on several occasions and it’s something that I am aware of,” Armstrong told the BBC. “It might have been a reason, maybe, why some of them didn’t want to play for Northern Ireland, in terms of whether they play for us or the Republic.
“I do think it’s something that needs to be talked about. Where it goes, I don’t know. It’s going to be down to the fans, the supporters’ clubs and the IFA as to what happens. But this is just one of the problems I’ve encountered over the last four months.”
Armstrong has held informal discussions with Snow Patrol songwriter and Northern Ireland fan Gary Lightbody about the anthem issue.
“I know Gary Lightbody and it was a possible way out. We looked at the Scottish solutions and the Welsh situations where they have their own national anthems.”
Armstrong, who comes from a nationalist background, acknowledged that the playing of God Save the Queen was “never” an issue for him during his Northern Ireland career.
“I don’t see why it should be a major issue now,’’ Armstrong said. “[But] it is an issue that has been raised by some — not by all.”