Negotiators are preparing to work through the weekend in a frantic effort to break the deadlock in the Brexit talks ahead of next's week crunch Commons vote.
EU officials are reported to have given the UK until Friday to come back with fresh proposals after talks earlier this week to end the impasse on the Northern Ireland backstop broke up without agreement.
With MPs preparing to vote on Tuesday, officials in Brussels were said to be ready to work through the weekend if the UK was able to present an "acceptable" plan, according to the BBC.
READ MORE: European Parliament to keep Scotland office after Brexit
The European Commission confirmed "technical talks" were continuing and said president Jean-Claude Juncker was "available 24/7" to meet Theresa May if a deal was close.
In the Commons, Attorney General Geoffrey Cox - who has been leading for the UK in the latest negotiations - said the talks would "almost certainly" carry on through the weekend.
In practical terms the Government needs an agreement by Sunday night at the latest as any new documentation relating to the deal must be published by Monday - the day before the vote.
Mr Cox and the Brexit Secretary Stephen Barclay are thought likely to return to Brussels on Friday in a final bid to secure an agreement ahead of next week's crunch vote.
It is thought that Number 10 is hoping a deal can be reached by Sunday night, with the possibility of the Prime Minister travelling to Brussels on Monday morning to meet European Commission president Jean-Claude Juncker.
Ministers were said to be braced for another heavy defeat on Tuesday after the previous "meaningful vote" was overwhelmingly lost by a majority of 230, with many MPs deeply unhappy about the backstop.
Mr Cox told MPs he was continuing to press for legally binding changes to the backstop - intended to prevent the return of a hard border on the island of Ireland - that would ensure the UK could not be tied indefinitely to EU rules.
He rejected claims that the Government had again failed to come forward with concrete proposals, insisting there had been "focused, detailed and careful discussions".
READ MORE: Brexit: UK given 48 hours to produce fresh proposals to break deadlock
"We are discussing text with the European Union," he said.
"I am surprised to hear the comments that have emerged over the last 48 hours the proposals are not clear. They are as clear as day and we are continuing to discuss them."
However there was clear frustration on the EU side, with chief negotiator Michel Barnier reportedly complaining that Mr Cox had produced "a legal solution to a political problem".
France's Europe minister Nathalie Loiseau said they were still waiting for a "sustainable proposal" from the British side.
"We have heard what you don't want, we are willing to know what you want. There were no precise proposals - there were ideas," she told the BBC Radio 4 Today programme.
Meanwhile, Chancellor Philip Hammond warned Tory Brexiteers they risk seeing Britain's withdrawal from the EU delayed if they vote down Mrs May's deal again.
He said he had a "high degree of confidence" that MPs would come back the next day to vote against Britain leaving without a deal.
"If the Prime Minister's deal does not get approved on Tuesday then it is likely that the House of Commons will vote to extend the Article 50 procedure, to not leave the European Union without a deal, and where we go thereafter is highly uncertain," he told the Today programme.
"For those people who are passionate about ensuring that we leave the European Union on time, it surely must be something that they need to think very, very carefully about now, because they run the risk of us moving away from their preferred course of action if we don't get this deal through on Tuesday."
However former Northern Ireland secretary Theresa Villiers, who backed Leave in the referendum, warned the Government appeared to be heading for another defeat.
"I suspect we will get the same result," she told BBC Radio 4's The World At One. "It really does depend on whether there is a last-minute breakthrough in the Geoffrey Cox work."
Earlier, Jeremy Corbyn said he was "more certain than ever" that MPs would back a deal to keep the UK closely tied to the EU after he held talks on Wednesday with senior pro-EU Tories.
The Labour leader met former ministers Sir Oliver Letwin and Nick Boles along with Labour MPs Stephen Kinnock and Lucy Powell to discuss their proposed "Common Market 2.0" plan which would keep the UK in the single market and the customs union.
Writing in the Daily Mirror he said he was confident they could "find a way to work across Parliament to force the Government to back a sensible Brexit plan that protects jobs".
"We will do whatever we can to find a solution that can unite the country so, together, we can face down the real challenges and seize the opportunities in this moment of great change," he said.
However the move risks infuriating Labour MPs who back a second referendum, after he last week said the party would support another public vote if it was unable to get its own Brexit plan passed.
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