Páirc Uí Chaoimh has been offered as an alternative venue for Euro 2028, the Tánaiste has said.
The Government has approached the FAI with the suggestion of using the Cork stadium after the British government announced last week that it would not fund the redevelopment of Casement Park in Belfast in time for the tournament.
Micheál Martin said the Government's €50m pledge to rebuild the stadium remains on the table and it is still the government's view that a stadium needs to be built at the site.
It is important that there is closure on the issue of Casement as the previous British government delayed a lot on the matter, Mr Martin said.
However, he said the possibility of hosting Euro 2028 fixtures in Cork has been raised with the powers that be.
"I think that people across the country would like the opportunity to watch the Euros," he said.
Mr Martin said there is an appetite for Ireland to improve its existing stadia and have the ability to host similar tournaments in the future.
Minister of State for Sport Thomas Byrne said he had spoken with the FAI about alternative venues in Ireland on Monday.
"We want to keep as many games on the island as possible. Croke Park has always been in the mix but UEFA decided not to have it," said Mr Byrne.
He acknowledged that both Páirc Uí Chaoimh and Croke Park would need work in terms of capacity but said these challenges are not insurmountable.
"I am conscious that there are other football associations involved in this and these discussions are ongoing. There is a lot of work done already by UEFA but I think it is important that we really fight tooth and nail to keep as many games as possible on the island," Mr Byrne said.
Cork City Councillor Peter Horgan had previously called for Páirc Uí Chaoimh to be used as part of the soccer tournament and welcomed the comments made by the Tánaiste.
Mr Horgan called for a whole of Government approach and expressed his hope that the other coalition parties would now follow suit.
"We can create a groundswell of support to shift the games now from Casement to Cork. I want to see Cork put up in lights for this European Championship," the Labour councillor said.
"We can do it by putting aside party politics issues, forgetting who gets the credit and securing it for the people of Cork and the wider Munster area. It would be seismic to have."
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