Ireland isn't part of an EU-wide deal to open borders to 15 countries across the globe.
On Tuesday, the EU released the names of 15 countries whose citizens could travel to member states from Wednesday.
But Ireland isn't included because it is not in the Schengen area of free travel and has a Common Travel Area with the UK.
It is understood that Ireland was invited to take part in the joint agreement.
However, it could only do that if Britain also agreed due to the open border.
The 'safe' travel list includes 15 nations - but excludes the United States, China, Russia and Brazil.
The European Council said travellers from Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay will be permitted to travel to the EU.
It has been suggested that the EU will allow passengers from China if the offer is returned.
The Irish Government continues to urge people not to make any non-essential trips abroad.
The Department of Foreign Affairs said: "The Irish Authorities advise against all non-essential travel overseas until further notice.
"This includes Great Britain but does not apply to Northern Ireland. It also includes all travel by cruise ship."
It comes as Chief Medical Officer Dr Tony Holohan urged people to consider cancelling any foreign holiday plans in the coming months.
When asked on Monday if people should consider opting out of foreign holidays, Dr Holohan told of his fears over the virus being "re-imported" back into the country.
He said: "We’d like people not to travel, yes.
“It makes much more sense to not go ahead with that booking and to risk travelling abroad, picking up this infection, risk for you, for any family member you be travelling with or indeed any close contacts you have.
"I think that would be not just in your individual interest but in our collective interest.”
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