The Government may cover the cost of European Health Insurance Cards (EHICs) for people in the North after Brexit.
The card gives citizens access to state medical treatment while travelling in the EU.
A no-deal Brexit would invalidate the cards for people living in the North.
However, Tánaister and Minister for Foreign Affairs Simon Coveney said: "When EU citizens travel across the EU they have health insurance cover.
Speaking in the Dáil today, he said: "We are working and will ensure that we extend that right to Northern Ireland.
"That will involve passing legislation here and it will involve the Irish Government, if necessary, paying for that insurance cover for citizens in Northern Ireland."