The Government may cover the cost of European Health Insurance Cards (EHICs) for people in Northern Ireland after Brexit.
The plastic gives citizens access to state medical treatment while travelling in the EU.
A no-deal Brexit would invalidate the cards.
Foreign affairs minister Simon Coveney said: "When EU citizens travel across the EU they have health insurance cover.
"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."