The FAI claims it is unaware of any change to Fifa rules permit players born in Northern Ireland to play for the Republic.
The Irish Football Association (IFA) today said it had been told by Fifa that any player born north of the border who wished to play for the Republic must meet certain criteria.
These include a requirement to play for up to two years without interruption south of the border or have close family members from the Republic.
An IFA spokeswoman said: "Fifa have said that if we deem any player called into the Republic of Ireland's squad ineligible then we can bring that case to Fifa.
"We can appeal if we think they are going against any of the criteria."
However, the FAI maintains it is allowed to pick Northern Ireland-born players, even if they do not have family ties with the south.
A spokesman said: "We do not believe there has been any change to Fifa's stated position that any player from Northern Ireland is eligible to play for either Northern Ireland or the Republic of Ireland."
The developments have prompted political reaction from both sides of the northern community.
SDLP Assembly member Dominic Bradley, who represents the border constituency of Newry and Armagh, says the decision is "totally out of keeping with the letter and the spirit of the Good Friday Agreement (which paved the way for political power-sharing in Northern Ireland).
"It seems totally ridiculous that somebody born in Newry, Co Down, as an Irish citizen, can't play for the Irish national team unless they have resided in the Republic for two years.
"They could be playing for Manchester United but would not be eligible to play for their country."
Democratic Unionist MP for East Derry Gregory Campbell argues that it provides welcome clarity and would regulate any inconsistencies.
"We should be working towards the position where people want to play for Northern Ireland," he said today. "Hopefully this can draw a line under it."
Controversy last year when the IFA protested after Derry-born Darron Gibson was picked for the Republic of Ireland team and featured in September's Euro 2008 qualifier against Slovakia in Bratislava, despite having represented the north at under-16 level.