A No 10 source says a Brexit deal is “essentially impossible” after a call between the PM and Angela Merkel.
Boris Johnson spoke to the German chancellor earlier about the proposals he put forward to the EU – but the source said she made clear a deal based on them was “overwhelmingly unlikely”.
They also claimed she said a deal would never be possible unless Northern Ireland stayed in a customs union.
But Labour called it a “cynical attempt to sabotage the negotiations”.
Shadow Brexit secretary Sir Keir Starmer said Mr Johnson “will never take responsibility for his own failure to put forward a credible deal”, and called on Parliament to “unite prevent this reckless government crashing us out of the EU”.
The BBC’s Brussels correspondent, Adam Fleming, said the German chancellery had not released their interpretation of the call, and it would be important to “compare and contrast”.
But he said an EU official close to the negotiations in Brussels had told him Mrs Merkel’s reported comments did not reflect the EU’s agreed position, adding: “This is not our language.”
Mr Johnson sent new proposals to Brussels last week, with the key focus being on replacing the so-called backstop – the policy negotiated by Theresa May and the EU to prevent a hard border returning to the island of Ireland – which has long been a sticking point.
After presenting the plans, government sources hoped the UK might be able to enter an intense 10-day period of negotiations almost immediately, with the aim of coming to a final agreement at an EU summit on 17 October.
But after the phone call, the No 10 source said it had been a “clarifying moment”, adding: “Talks in Brussels are close to breaking down, despite the fact that the UK has moved a long way.”
They said the UK was not willing to move away from the principle of providing a consent mechanism for Northern Ireland or the plan for leaving the customs union, and if the EU did not accept those principles, “that will be that” and the plan moving forward would be an “obstructive” strategy towards Brussels.
They also accused the EU of being “willing to torpedo the Good Friday agreement” – the peace process agreed in Northern Ireland in the 1990s by refusing to accept Mr Johnson’s proposals.
The government argues allowing Stormont to approve part of the PM’s plan is key to respecting the so-called “principle of consent” in the Good Friday Agreement, but Irish Prime Minister Leo Varadkar has warned it could actually undermine that principle by giving one party in Northern Ireland a veto over what happens to the country as a whole.
Mr Johnson has insisted the UK will leave the EU on the Brexit deadline of 31 October, with or without a deal. That is despite legislation passed by MPs last month known, as the Benn Act, which requires Mr Johnson to write to the EU requesting a further delay if no deal is signed off by Parliament by 19 October – unless MPs agree to a no-deal Brexit.
On Monday night, the Spectator published texts from a Downing Street source, who claimed if the deal “dies in the next few days, then it won’t be revived”.
The government has not denied the briefing, which also said Mr Johnson “will do all sorts of things to scupper a delay” to leaving the EU.
Earlier, the BBC’s political editor Laura Kuenssberg said there was a growing expectation in government Brexit talks would fail before the week was out.
EU diplomats have told Adam Fleming there has been “zero progress” in the talks and in some areas they believe things are going backwards.
Under Mr Johnson’s proposals, which he calls a “broad landing zone” for a new deal with the EU:
After receiving the proposals, the EU pledged to examine them carefully.
But a number of senior figures, including Mr Varadkar, warned the proposals did not form the basis for deeper negotiations – even if they believed a deal could still be done.
French President Emanuel Macron said the EU would decide at the end of the week whether a new deal was possible.
But a leaked presentation to EU diplomats revealed they were unwilling to accept the UK’s plans committing to no checks on either side of the Irish border if the Northern Ireland Assembly – Stormont – is granted a veto and there is no guarantee of checks on the UK side.
BBC Brussels correspondent Adam Fleming said EU negotiators were “so nonplussed by the proposal they asked if it was a mistake”.
It is understood the UK also wants continuing access to several EU trade databases, even if Stormont withholds its consent for the new arrangements.