The Brexit negotiations are at a crucial stage, with the Irish border being a key sticking point.
May in December agreed in principle to a binding "backstop" to ensure a soft border irrespective of future EU-UK ties, but later balked at an EU proposal to achieve this by treating Northern Ireland as a separate customs area to the rest of the United Kingdom.
The Irish government, which has said it has concerns about May's white paper, on Friday said a backstop was essential, but could be renegotiated so long as it was better than the current deal and legally operable.
"And, on that basis, I look forward to resuming constructive discussions".
With the Irish border set to become the only land barrier between the United Kingdom and European Union, frustration is growing in Dublin, Belfast and Brussels as United Kingdom negotiators struggle to find a solution which avoids customs checks or even CCTV cameras on the border - a potentially explosive development on the politically sensitive frontier. In my view, it's take this seriously or we are heading for no deal. "We can't solve it on our own, but nor can we wash our hands of any responsibility for it, so we must work together to solve it".
Speaking at the city's Waterfront Hall, she is due to say that any such deal would go against the Good Friday Agreement, which brought peace to Northern Ireland 20 years ago after decades of conflict.
"Not to seek a solution would be to resume our career as an independent sovereign trading nation by betraying commitments to a part of our nation and to our nearest neighbour".
Earlier this month two of May's top Cabinet ministers - Brexit secretary David Davis and Foreign Secretary Boris Johnson - quit over what they see as a watering-down of the UK's blueprint for Brexit.
In further comments ahead of her visit, Mrs May added: "From the start of the negotiations, the UK Government has put Northern Ireland's unique circumstances at the heart of our negotiations".
After quitting the cabinet, former Foreign Secretary Boris Johnson singled out her treatment of the border as the biggest mistake of her negotiations with the European Union for a smooth exit from the bloc next year.
Her bottom line, she will never accept such a proposal and believes no British Prime Minister could ever accept it.
Amid the ongoing power-sharing impasse at Stormont, Mrs May is meeting the five main political parties on her two day visit to Northern Ireland, which included her first visit to the Irish border since the Brexit referendum. Twenty years after the Good Friday Agreement, the return of any form of physical checkpoints or other infrastructure would be "an alien concept".
As EU27 ministers gathered in Brussels, there were signs of concern that the recent turmoil at Westminster might make it more hard to achieve an orderly withdrawal.
Mr Varadkar said while his government continued to make contingency plans for a hard Brexit, he stressed authorities were not planning for a hardened border.
Stating her determination to complete what we have started in Brexit talks, Mrs May will say: We can negotiate a new relationship with the European Union that works in our mutual interest.