A British request for a Brexit deadline extension as well as consequences of a chaotic no-deal will be discussed between Taoiseach Leo Varadkar and French President Emmanuel Macron today.
The Government has so far declined to say what checks or trade arrangements could fall into place if Britain leaves without a deal and there is no border.
However, Mr Macron is expected to discuss this with Mr Varadkar today.
In a statement ahead of travelling to Paris, the Government said the two leaders would discuss the latest developments in Westminster.
Other sources said the issue of what happens with a no-deal would be on the table at the Elysee Palace meeting.
Mr Varadkar said: “I’m looking forward to meeting President Macron at this critical juncture in Brexit.
"I will thank him for the ongoing solidarity from France, including the clear commitment that the withdrawal agreement must include an operational backstop to avoid a hard border.
I am keen to discuss the possible scenarios arising from this week, particularly how the European Council should respond to a request for another extension, should there be one, and ongoing efforts to secure ratification of the withdrawal agreement.
"As I have indicated, it is now up to the UK to show how it plans to proceed and avoid a no-deal scenario. We are preparing for all outcomes, and have prepared intensively for a no-deal.
"But no one should under-estimate the difficulties that a no-deal will present, for all of us.”
Mr Varadkar will also meet German chancellor Angela Merkel in Dublin on Thursday, at which similar issues are expected to be discussed ahead of another emergency EU leaders summit in Brussels next week.
The Government continues to say that it will not seal the border if there is a no-deal Brexit but that there is still no fallback plan on how to protect the EU’s single market.
EU Brexit negotiator Michel Barnier said in January that there would be inspections on foods or goods moving through Ireland with a disorderly Brexit: “How should we control animals crossing the border? There will have to be checks.”
Nonetheless, specifics on this have yet to be made public by the Government.
Taoiseach Leo Varadkar has only said to date that discussions have been had on the issue and nothing has been documented.
Meanwhile, Sinn Féin leader Mary Lou McDonald met Mr Barnier in Brussels yesterday over the need to protect Irish citizens and the economy in the event of a disorderly Brexit.
Despite this, she also said it is “not clear” what would happen with a no-deal Brexit.
Elsewhere, Labour finance spokesperson Joan Burton has expressed surprise at a lack of estimates from the Revenue Commissions of tax and duty losses from smuggling in the event of a no-deal Brexit.
This follows a series of Dáil questions tabled by Ms Burton, which returned no detail.
She said: “I have been asking the minister for finance and the Revenue Commissioners a series of questions about the number of customs officers, their training, and the potential losses in the event of a no deal Brexit.
"As the worst outcome becomes possible, we have no certainty on the type of controls or checks that will happen with cross border trade or whether it will be carried out in ports, and at factory gates.”