The club recently parted ways with Nathan Jones after just nine months in charge and have been looking for a replacement, with news of an approach for O'Neill breaking on Thursday afternoon.
O'Neill is now preparing his side to face Netherlands and Germany next week in the European Qualifiers and, although they can still qualify through Group C, a play-off in March is more likely.
Stoke now find themselves bottom of the Championship, having lost 11 of their first 15 matches in the league this season.
They have won just two of their last 15 games in the league leaving them rooted to the bottom of the table and already six points from safety.
However, they have a number of well-known players such as internationals Jack Butland, Joe Allen and James McClean.
"It is always flattering".
Regardless of those results a play-off place seems likely for Northern Ireland, which will surely factor into the 50-year-old's thinking as he ponders the prospect of taking over the Championship strugglers. "It is better to be linked than not linked, let's be honest", he said. "But right now, my focus is obviously on the two games that lie ahead".
After that, they were denied a World Cup finals spot only by a highly contentious play-off defeat to Switzerland and are now highly likely to feature in the Euro 2020 play-offs in March. O'Neill has been the Northern Ireland coach since December 2011.
Michael O'Neill has helped Northern Ireland rise as high as 20th in the Federation Internationale de Football Association world rankings.