A flurry of diplomatic meetings over the weekend had raised hopes for an agreement on Britain's divorce from the bloc.
The border between Northern Ireland the Republic of Ireland remains biggest sticking point in negotiations.
The PM met with Sinn Fein leader Mary Lou McDonald and vice president Michelle O'Neill and "reaffirmed her commitment to there being no hard border between Northern Ireland and Ireland and no border in the Irish Sea", Downing Street said.
She added: "This backstop arrangement would not be temporary".
The former attorney general, speaking after Mrs May updated MPs on Brexit negotiations, said: "I wish (Mrs May) every good thing in this negotiation, but I do point out to her that we are heading towards a conclusion where we are going to be in at least a two-year relationship with the European Union, which is a condition of vassalage because we have absolutely no say in the rule-making that we are tied to".
Opposition Labour leader Jeremy Corbyn blasted May's approach, saying "the Prime Minister's failure to stand up to the warring factions on her own side have led us to this impasse". One proposal is to keep the United Kingdom inside the EU's customs union on a temporary basis, which would mean no new checks on goods passing from Northern Ireland to Ireland would be needed. The DUP said it will not accept any deal that results in Northern Ireland being treated differently from the rest of the UK.
Both London and Brussels are seeking to ensure there is no hard border in Ireland.
But a spokesperson for May said there were "a number of means of achieving what we want to achieve" on the backstop.
One diplomat said on condition of anonmyity that the ambassadors' meeting could suggest a breakthrough, while another said it could signal there had been no agreement.
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Barnier met his British opposite number Dominic Raab in Brussels on Sunday, but they failed to agree a draft Brexit divorce arrangement before European Union leaders arrive in the city on Wednesday.
So even if May strikes a deal with Brussels, she will struggle to get it past her government and Parliament at home.
German Chancellor Angela Merkel said Berlin wants the UK's withdrawal next March to be orderly "but not at any price".
Rogers, who quit his post a year ago, said both May's plan, which would keep Britain in the European Union single market for goods, and rival Boris Johnson's vision of a looser free-trade deal have "precisely zero" chance of being accepted by the bloc.
That timetable - which markets have started to price in - has been thrown off and there's likely to be more talk of how to prepare for a chaotic and acrimonious no-deal split.
Britain refuses to be pinned down on a date for a deal.
"The idea that we would try and stop commercial traffic crossing that when you don't even know when you're crossing the border today because it's so seamless".
Foreign Secretary Jeremy Hunt insisted that ministers would not sign up up to any plan which compromised the territorial integrity of the United Kingdom by imposing a "border in the Irish Sea".
After meetings in Brussels earlier this week, the DUP issued a series of terse warnings to May over the compromise that is in the making between the European Union and British negotiators.
Irish Prime Minister Leo Varadkar said Monday that "I figure November or December is the best opportunity for a deal".