Irish Prime Minister Leo Varadkar echoed Merkel's words saying that it will be hard to establish a deal by next week.
But said: "I must note that there has been no progress".
Emmanuel Hemmings, a 45-year-old Briton from the West Midlands, told The Associated Press: "We expect the European Union to say that Johnson's proposals don't make sense and should not be pursued".
"She made clear a deal is overwhelmingly unlikely and she thinks the EU has a veto on us leaving the customs union", the source, quoted by Sky News, said.
One source in Johnson's office told The Spectator magazine the government will try to "do all sorts of things" to prevent another Brexit delay should negotiations really collapse.
Mr Varadkar added that it was his job to hold the United Kingdom to commitments it had made since the 2016 referendum to prevent a hard border on the island of Ireland and uphold the Good Friday Agreement.
The latest comments from Downing Street follow a warning that negotiations with Brussels to enable Britain to leave at the end of October with a deal would "probably" end this week. The official said Britain's security relationships would be scaled back and any country backing a postponement would be at the "bottom of the queue" for future co-operation.
'Those who supported the delay will face the inevitable, being seen to interfere in domestic politics by colluding with a parliament as popular as the clap.' The outburst led Northern Ireland secretary, Julian Smith, to stress nothing should be done to jeopardise security co-operation with Dublin.
Scottish First Minister Nicola Sturgeon, who opposes Brexit, tweeted: "The UK government's attempts to shift the blame for the Brexit fiasco to anyone but themselves - today it's Merkel - is pathetically transparent". "It reveals that there doesn't appear an actual plan at all".
The EU denied its position had changed.
"Boris Johnson will never take responsibility for his own failure to put forward a credible deal".
"Clearly some market participants had not given up hope until the last moment that the British government and the European Union would be able to agree on an exit agreement before the European Union summit in just under two weeks' time", says Thu Lan Nguyen, an analyst with Commerzbank. In Berlin, a spokesman for the German government confirmed to AFP the two leaders had spoken but said he would not comment on the content of the call.
"No UK government could ever concede such a surrender".
Speaking at a regular press briefing, the spokesperson said the European Union position "has not changed: we are working for a deal" and added that as technical talks continue today she does not see "how the talks could have broken down".
"This will help to ensure that companies have the necessary customs paperwork in place for border arrangements ahead of Brexit on 31 October, if we leave without a deal", the plans said.
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