The Taoiseach is expected to speak with British Prime Minister tomorrow morning, after British MPs authorised Theresa May to go back to Brussels and try to renegotiate her Brexit deal.
Leo Varadkar was in contact with the British Prime Minister earlier today ahead of the votes in the House of Commons.
Mr Varadkar said he had agreed to speak again with Mrs May after the votes in Westminster to see "what the next steps are".
While decisions being made in Westminster this evening will impact on Ireland and the Irish people, North and South, the personal relations between the British and Irish Governments remain strong, said Tánaiste Simon Coveney.
Mr Coveney was responding to opposition questions in the Dáil.
Minister Coveney said new relationship structures post-Brexit between Britain and Ireland will be confirmed at the next meeting of the British Irish Inter-governmental conference.
Minister Coveney said plans will be made for future annual meetings between both governments led by the Taoiseach and Mrs May involving other ministers.
He equated it to the kind of structure that France and Germany and Spain and Portugal have.
"That's the structure we want to see in the future to build on structures already there through the Good Friday Agreement," he said.
Earlier, the Cabinet discussed the economic impact of a no-deal Brexit.
Minister for Finance Minister Paschal Donohoe brought a document to Government this morning that gives his Department's latest analysis.
It is likely to revise the forecasted economic growth figures that would follow on from a hard Brexit.
In the Budget last year, Mr Donohoe spoke about economic growth of 4.2% this year.
But that was based on a Brexit deal and a transition period.
However, the most updated assessment will lower that figure after the National Institute of Economic and Social Research in Britain examined the impact of a no-deal Brexit there.
This suggested that the effects could be more damaging than was initially thought and it has led to a change in the Irish Government analysis too.