The Prime Minister will use a speech in Belfast on Friday to reiterate her refusal to contemplate any backstop deal that treats Northern Ireland differently from the rest of the UK.
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.
Mrs May will say that following the publication of the Government’s white paper agreed at Chequers, it is “now for the EU to respond”.
She will add: “Not simply to fall back on to previous positions which have already been proven unworkable. But to evolve their position in kind.
“And, on that basis, I look forward to resuming constructive discussions.”
The EU’s other 27 states will have a chance to examine and respond to the white paper when its General Council of ministers meets in Brussels on Friday morning.
They will also receive an update on negotiations from the European Commission’s chief negotiator, Michel Barnier.
The Irish border issue is one of the most disputed parts of the Brexit negotiations.
In the event of a hard no-deal Brexit, the EU wants a backstop that would effectively create a border down the Irish Sea between the island of Ireland and Great Britain, something Mrs May has repeatedly opposed.
The UK Government insists that any backstop position should include the UK as a whole.
Her speech comes the day after new Brexit Secretary Dominic Raab headed to Brussels for the first time to take part in talks with Mr Barnier.
Mr Barnier told reporters on Thursday that it was “a matter of urgency to agree a legally operative backstop”, saying: “We need an all-weather insurance policy.”
Mr Raab said that he was looking forward “with renewed energy, vigour and vim” to seeing the detail of the White Paper hammered out after a gruelling Cabinet conclave at Chequers.
Brexiteer Commons Leader Andrea Leadsom put some pressure on Mrs May’s plan, saying the EU must be told the Chequers blueprint, which has divided the Conservative party, is the “final offer” rather than an opening gambit.
However she also admitted quitting without an agreement would not be an “optimal solution”.
Foreign Secretary Jeremy Hunt, meanwhile, insisted the deal is “absolutely alive” despite the Government being forced to make concessions to Brexiteers.
Mrs May will again refuse to countenance any backstop that creates a divide between Northern Ireland and the rest of the UK.
“The economic and constitutional dislocation of a formal ‘third country’ customs border within our own country is something I will never accept and I believe no British prime minister could ever accept.
“And as they made clear this week, it is not something the House of Commons will accept either.”
As the EU warns member states to increase preparations for no deal, the Prime Minister is also due to insist that an agreement can be reached with Brussels “that works in our mutual interest”.
She will say the deal will put the UK on the way to “a prosperous future, protecting jobs and boosting prosperity” at the same time as honouring the 2016 referendum result, adding: “I am passionate about that brighter future and the possibilities that are within our grasp.”
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.
She held talks with her Westminster confidence and supply partners, the DUP, on Thursday evening, an engagement that included a private dinner with leader Arlene Foster and deputy leader Nigel Dodds in Co Fermanagh.
Mrs May also held talks with an SDLP delegation.
On Friday morning she will meet Sinn Fein, the Ulster Unionists and Alliance Party.
Ahead of the meeting on the outskirts of Belfast, Sinn Fein President Mary Lou McDonald heavily criticised Mrs May’s handling of the Brexit process.
“The British government’s Brexit chaos has been marked by prevarication and stalling, ever changing positions and broken agreements,” she said.
“This situation is intolerable and unacceptable.”
A number of protests took place outside the Crescent Arts Centre where Mrs May was visiting on Friday morning.
Campaigners from victims and survivor groups of the Troubles, Irish language activists and Sinn Fein politicians held banners and placards.
Sinn Fein Senator Niall O Donnghaile said: “There’s a broad range of groups here and that represents the broad range of issues outstanding in our society, and the broad range of commitments made by the British Government that still remain unfulfilled.
“That ranges from an Irish Language Act, legacy issues, women’s reproductive health, marriage equality - they’re all represented here.
“We hope Theresa May gets the message when she’s here that everything isn’t rosy in the garden.”