Other sources familiar with Barnier's meeting with European Union ambassadors confirmed this, and one added that "certain countries insisted that preparations for a "no deal" be accelerated".
And she lashed the EU's "backstop to a backstop" to the thorny issue of the Irish border, which would leave Northern Ireland tied to the the bloc's customs and some single market rules if no free trade deal is done in time.
The impasse threatens to throw into disarray carefully choreographed plans which would have seen European Union leaders meeting in Brussels on Wednesday give the green light to a special summit in November to finalise the terms of the UK's withdrawal from the bloc.
And even though, the European Union have agreed to explore a UK-wide customs solution to the backstop, two problems remain, Theresa May told the MPs, at which point the parliamentarians burst into laughter.
The Cabinet will meet on Tuesday morning to discuss the state of Brexit negotiations before May travels to Brussels on Wednesday evening.
A few days later, he was joined by another vocal Eurosceptic minister, Boris Johnson, who stepped down as Foreign Secretary and has since issued a series of direct attacks on the British PM's plans over the issue of Brexit. Arlene Foster, the head of the Northern Irish party that props up her government, was quoted as saying she expects a no-deal exit because May's proposals on the Irish border are unacceptable.
May has insisted that she would never agree to the EU's proposal, which would separate Northern Ireland constitutionally and economically from the rest of the UK.
Britain's global trade, environment and Brexit ministers told May at a meeting on Thursday that they fear the whole of Britain could remain in the EU customs union for an open-ended period, the BBC said.
But negotiations ended without a breakthrough, including on the issue of trade to and from Northern Ireland, which has emerged as a possible deal breaker and even a threat to Prime Minister Theresa May's leadership.
Mrs May insists such an arrangement must apply to the whole of the United Kingdom to avoid the creation of a "border in the Irish Sea" between Northern Ireland and the rest of the UK.
Lobbying of May from all sides of the Brexit debate has increased in recent weeks as London and Brussels edge closer to an agreement on a draft withdrawal treaty to cover the divorce terms, a transition period and a solution for Northern Ireland.
The Irish border issue remains unsolved.
May must also overcome considerable opposition to her Brexit plan from within her own party. So it must be the case that the backstop should not need to come into force and second - if it does, it must be temporary.
She said that she could never accept a border down the Irish Sea.
During the parliamentary session, key Brexiteers, including former party leader Iain Duncan Smith, sought to pin her down on a commitment to an absolute deadline for any backstop to end, which Mrs.
The DUP vehemently opposes any checks between Northern Ireland and mainland Britain after Brexit, which is due in March and would be the United Kingdom's biggest trade and foreign policy shift for more than four decades.
As I have said many times October 2018 was going to be a big month but it looks like it might be bigger than I thought.
The week before, the Office for Budget Responsibility (the government's economic forecaster) warned that a no-deal Brexit would trigger border delays, which, in turn, could lead to companies and consumers stockpiling food and other supplies, including medicine.