Should O'Neill become Scotland manager, he would have an ever closer relationship with Rodgers as Celtic now supply more players than any other club to the national team.
The FAW wants to retain Coleman, who came close to leaving for Hull City past year, but, in order to remain, he would first need to secure certain commitments.
Celtic manager Brendan Rodgers believes compatriot Michael O'Neill would have plenty to work with if he took over as Scotland manager.
The SFA made a formal approach to the Irish FA for O'Neill this week and it's understood the 48-year-old wants the opportunity to speak to Hampden bosses about the vacancy.
O'Neill is under contract until June 2020 but he may be open to a new challenge after tasting World Cup play-off heartbreak against Switzerland.
He said: "Anything linking me to the job is purely speculation because the Northern Ireland job isn't available right now".
Brandon Peters leaves game with injury
Defense from both sides dominated the first quarter, with Wisconsin taking a 7-0 lead on a 50-yard punt return touchdown. That led to a 39-yard field goal, giving MI a 10-7 lead with 6 minutes, 36 seconds remaining in the third quarter.
"But it's down to him if he wants to stay at Northern Ireland or go back to club football".
Stephen Robinson has admitted it would be a "massive honour" to manage Northern Ireland if O'Neill leaves.
Scotland have not been to a major tournament since the 1998 World Cup.
"For me, like the Rangers job, Derek McInnes and him would be obvious standouts, but I really hope Tommy gets the chance, given the work he has done, to do it on a bigger stage, wherever that is".
"It would be a natural progression for any manager with ambitions to see your own national team job as the most important one of them all".
"He knows that it is like any Scottish manager, if they were linked to the Scottish job, your country is your country, and for me it is the top job that I could probably ever achieve".