The absence of a single market border in Ireland could possibly result in checks at ports in France or the Netherlands if there is a no deal Brexit.
It is understood this warning came from the Taoiseach in a private meeting with party leaders tonight.
Sources have indicated that it was one of the options mentioned in a discussion around what might happen if there is no withdrawal agreement.
This would mean that border control would be moved away from Ireland and on to mainland Europe.
A Department of Foreign Affairs Spokesperson said last night that there is at this point a hard won agreement that delivers a sensible Brexit ratified by 27 nations and the Irish Government is focused on the need for Westminster and the British Government to make a decision.
