The Taoiseach says there remains a possibility of All Ireland championships this year.
Leo Varadkar was speaking on the The Late Late Show following the publication of the government's Roadmap for Reopening Society and Business on Friday night.
The document allows for team sports to resume on July 20th, provided it's safe to do so.
When asked about the GAA's potential to play All Ireland finals this year, the Taoiseach told host Ryan Tubridy, "There’s a possibility of an All Ireland this year...but not with spectators".
The GAA are yet to comment on Varadkar's roadmap.
GAA president John Horan recently stated that the association would not make any rushed decisions about a return to play, maintaining that the club game must be the first to return.
It's believed a lack of All Ireland championships could cost the GAA around €15million.
The FAI say they "will move to evaluate the implications and update stakeholders from all strands of football as soon as feasible".
The SSE Airtricity League has been on hold since early March as a result of the COVID-19 pandemic.
An FAI statement on Friday night read:
The Association will now examine what this lockdown extension and the guidelines published in the Government’s ‘Roadmap For Reopening Society and Business’ mean for all stakeholders at all levels of the game. The FAI will move to evaluate the implications and update stakeholders from all strands of football as soon as feasible.
The decision to extend the cessation order for all football until May 18thhas been taken in light of the COVID-19 pandemic and in the best interests of our players, coaches, volunteers, supporters and staff.
FAI Medical Director Dr Alan Byrne has again advised the FAI that in the current exceptional circumstances, clubs should not engage in collective training during the cessation period for all football activity under the FAI’s jurisdiction.
The FAI is in constant communication with the Department of Health and UEFA on COVID-19 and will continue to follow all government guidelines.The Association advises all members, volunteers and stakeholders to respect the HSE guidelines on social distancing during this pandemic.
The Association also appeals to everyone involved with Irish football to stay at home over the May Bank Holiday weekend.