As the Taoiseach prepares to meet the European Council President later today, a new report claims a hard border is 'inevitable' after Brexit.
A committee of British MPs says pulling out of the single market and the customs union would make it impossible to achieve a "frictionless" border.
Leo Varadkar and Donald Tusk will discuss the issue in Dublin later ahead of a crucial EU Summit later this month.
Speaking a week ago, Mr Tusk insisted European leaders needed to see progress from the UK 'within 10 days'.
Sufficient progress in #Brexit talks at December #EUCO is possible. But still a huge challenge.
We need to see progress from UK within 10 days on all issues, including on Ireland. pic.twitter.com/NKe86zGo17
— Donald Tusk (@eucopresident) November 24, 2017
Theresa May is meeting with European Commission president Jean-Claude Juncker on Monday, when she hopes to strike an agreement on the key withdrawal issues of money, citizens rights and Ireland.
If progress is agreed, EU leaders will then sanction the second phase of Brexit talks at a key summit on 14/15 December.
But Ireland has recently demanded a written guarantee there will be no hard border before agreeing negotiations can move onto transition arrangements and trade talks.
The Democratic Unionist Party (DUP) has indicated they'd pull their support for the British government if Northern Ireland is given different treatment to the rest of the UK.
DUP MP Sammy Wilson told BBC: "If there is any hint that in order to placate Dublin and the EU, [the British government is] prepared to have Northern Ireland treated differently than the rest of the United Kingdom... then they can't rely on our vote."
Tánaiste and Foreign Affairs Minister Simon Coveney, meanwhile, says a solution for everyone needs to be found.
He argued: "We will listen to what everybody has to say in Northern Ireland - regardless of where they come from, regardless of their community, regardless of their political party."
After DUP saying he needs to crane his neck back in, Simon Coveney says border issue is not a case of Orange vs Green pic.twitter.com/sgU6tK376z
— Sean Defoe (@SeanDefoe) December 1, 2017
Brexit committee report
In their new report, although not backed unanimously by the committee's members, MPs warn they "do not currently see how it will be possible" to avoid a customs border on the island of Ireland, if the British government pushes ahead with its aim to leave the single market and customs union.
British ministers' proposals for avoiding such a scenario are branded "untested and speculative" by the committee.
Their warning comes as the Irish border emerges as a critical hurdle in deadlocked negotiations, although one prominent pro-Brexit member of the committee branded the report's content as "old Remoaner arguments and fears".
The Brexit committee is also calling for both the EU and the British government to ensure an agreement on citizens' rights is "ring-fenced" when reached, so that it is preserved even if no overall divorce deal is agreed.
And the MPs want ministers to publish a white paper on its proposed transition period as soon as possible after this month's summit, as well as specific details of what the government hopes for in a long-term EU-UK trade deal.
'Untested and speculative proposals'
The committee's chair, Labour MP Hilary Benn, said: "Our report concludes that we cannot at present see how leaving the customs union and the single market can be reconciled with there being no border or infrastructure.
"Even by their own admission, the Government's proposals are untested and speculative, so it has yet to set out how no border can in practice be maintained with the UK outside the single market and the customs union."
He added: "Ministers assured us that detailed arrangements for the implementation period could be published by March 2018. This deadline must be achieved."
However, Brexit-backing members of the committee pointed out the report was only agreed by those MPs who supported Remain at last year's EU referendum, with five Leave-supporting MPs voting against its publication.
Conservative MP Jacob Rees-Mogg said: "The report was carried entirely by the votes of members who wanted to remain in the EU.
"Inevitably it has wheeled out all the old Remoaner arguments and fears. It does not represent the positive view of Brexit that many people now take."