The Irish FA will have to go to the Court of Arbitration for Sport if it wants to continue its row with the FAI over player eligibility.
NI-born Darron Gibson elected to play for the Republic of Ireland
Both the Northern Ireland and Republic of Ireland football bodies claimed victory on Saturday after Fifa said current rules would stay "unchanged".
A Fifa spokesman was unable to shed any further light on the issue on Sunday.
"If there is a real dispute...they will have to submit it to the Court of Arbitration," said Andreas Herren.
The issue centres on the Republic of Ireland's governing body's assertion that it is allowed to pick Northern Ireland-born players, even if they don't have family ties with the south.
Controversy arose earlier this year when the Irish FA protested after Derry-born Darron Gibson was picked for the Republic of Ireland team.
A communique issued after FIFA's meeting in Japan on Saturday did not clarify the matter, with just one sentence referring to the eligibility row.
"The Executive Committee decided to leave the current regulations regarding the eligibility of players to represent association teams unchanged," the governing body said.
Fifa spokesman Herren was reluctant to get drawn into what conclusions could be drawn from Saturday's statement.
We have submitted all kind of proposals and had all kinds of meetings to discuss the matter at length with both associations
Fifa spokesman Andreas Herren
"There's not a great deal to say. It's the status quo as before," the Fifa spokesman told BBC Sport.
"I'm not all that familiar with the intricacies of the Northern Irish/Ireland rules but the fact is, nothing has been changed by the executive committee (of Fifa).
"They stated that no specific regulations applied because both associations refused previous proposals by Fifa.
"If eventually there is a real dispute between those two associations on the eligibility then they will ultimately have to submit it to the CAS, the International Court of Arbitration in Sport in Lausanne."
Herren added that Fifa's executive committee "did not go any further into the Northern Ireland/Ireland matter".
The Fifa official denied that the world governing body has effectively "washed its hands" of the controversial Irish row.
"I would refute that completely and categorically.
"No one in his right mind can claim that after Fifa had been dealing with this matter for more than one year.
"We have submitted all kind of proposals and had all kinds of meetings to discuss the matter at length with both associations (and) come to the conclusion that none of the proposals that Fifa had submitted was accepted by either party."
The Fifa official's comments are certain to be a huge disappointment to the Northern Ireland governing body.
The IFA was convinced that Fifa had ruled in its favour only for the Republic's governing body to claim exactly the opposite later on Saturday evening.
"Senior Fifa sources have confirmed to us that the status quo remains and the FAI may continue to select players born in Northern Ireland," said the FAI.
An FAI spokesman added: "In October 2006, Fifa's Legal Department ruled that players born in Northern Ireland are entitled to play for the Republic of Ireland if they choose."
Earlier, IFA president Raymond Kennedy had said:"I was always quietly confident. Fifa is just upholding its own rules."
On-loan Wolves midfielder Gibson recently played for the Republic in a Euro 2008 qualifier.
He was born in Londonderry in Northern Ireland but elected to switch to the Republic after representing the north at Under-16 level.
Northern Ireland's political parties have got involved in the controversy and the Republic of Ireland's Foreign Minister Dermot Ahern also said that Northern Ireland-born players should be allowed to play for the Republic, if they wished.
Unionist politicians claimed that Fifa rules allowing Northern Ireland-born players to play for the Republic could "sectarianise" the Northern Ireland team.