However, one of Barnier's team reportedly told diplomats last week that a deal is "very close" as a result of new United Kingdom proposals on the Irish border "backstop" - the final major outstanding issue standing in the way of the Withdrawal Agreement being finalised.
May gathered selected members of her cabinet late Thursday to update them on the Brexit talks, and the Financial Times reported that she told them that a deal was drawing closer.
Britain's Prime Minister Theresa May attends a roundtable meeting with business leaders whose companies are inaugural signatories of the Race at Work Charter at the Southbank Centre in London, Britain, October 11, 2018. High stakes at high noon for these Brexit negotiations.
However, according to The Daily Telegraph the Government are planning to offer the DUP more money for Northern Ireland in return for their support.
Blasting the proposed deal, she said: "Trade from Great Britain into Northern Ireland would be in danger of restriction".
However, Mrs Foster said the EU's proposals would place "an effective one-way turnstile" between Northern Ireland and the rest of the UK.
British and European Union negotiators are understood to have agreed in principle to an all-UK backstop plan to avoid a hard border in Northern Ireland that would remove the final major obstacle blocking a withdrawal agreement. "There is no breakthrough - yet", Margaritis Schinas, chief spokesman for the EU's executive European Commission, told a news briefing on Thursday. He said it could result in three scenarios: going back to Brussels to renegotiate, holding a general election, and a referendum.
The 27 states remaining in the bloc hope to announce "decisive progress" in divorce talks at an European Union summit next week and then finalise their offer of close future ties with Britain next month.
The deal believed to be on the table involves keeping the whole United Kingdom in an "arrangement" that effectively preserves the existing EU customs union, ensuring the goods continue to move freely over the Irish land border regardless of the future trade relationship between London and Brussels.
He added that the DUP could vote down the Budget but still support the government in a confidence vote, as long as it changed its approach to Brexit.
Northern Ireland would also remain in the single market for goods.
The DUP has 10 MPs, although Ian Paisley can not vote in the Commons until November 20 after being suspended for failing to declare two family holidays paid for by the Sri Lankan government.
The OBR, an independent non-departmental public body, said it was "next to impossible" to predict the consequences of a no-deal Brexit.