It comes after fevered speculation that Northern Ireland could remain in the single market to solve the border issue with the Republic - a prospect strongly resisted by the DUP who said they would not accept any separation with the rest of the UK.
A meeting on this with all political party leaders is set for lunchtime today.
Irish state broadcaster RTE said that a draft text would commit Britain to "continued regulatory alignment" with the European Union to avoid divergence on the two sides of the Irish border.
Speaking at a joint press conference in Brussels with Mr Juncker, Mrs May said: "We have been negotiating hard".
Nadine Dorries, a member of Britain's ruling Conservative Party who supports Brexit, said May should tell European Union officials time is running out to move talks on to the next phase.
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May met with EU Commission President Jean-Claude Juncker and will later speak with EU Council President Tusk amid hopes to make progress on the questions of Britain's exit bill, the Irish border and the rights of citizens.
The concession has yet to be accepted by the Irish government.
"We had an agreement this morning", Irish Prime Minister Leo Varadkar said, expressing disappointment at the last-minute glitch.
The EU and the United Kingdom are nearing agreement on some divorce terms, including the size of the bill that Britain must pay as it leaves and the rights of citizens affected by Brexit. "We have common understanding on most issues".
If a Brexit deal can be done that "effectively" keeps Northern Ireland in the single European market, there is "surely no good practical reason" why Scotland should not benefit from such an arrangement, the First Minister has said. "Getting closer to sufficient progress", he said.
"We are negotiating the British withdrawal as a bloc of the European Union 27 and the other 26 European Union member states will only agree to a solution if the Irish government is in favour", the German MEP, a member of Angela Merkel's CDU party, told ITV.
And he added: "Despite our best efforts and significant progress we and our teams have made over the past days on three remaining withdrawal issues it was not possible to reach a complete agreement today".