The Downing Street official quoted Ms Merkel as saying that a deal now looked "overwhelming unlikely", and added that the Brexit talks were "close to breaking down". Brexit supporters say this can be managed by doing checks on goods away from the border, but critics say it will be hard to police this without any physical infrastructure like border posts of cameras, which could raise tensions in the divided communities of Ireland.
United Kingdom proposals released last week would see the introduction of a temporary all-island regulatory zone under which Northern Ireland would come out of the customs union but follow EU rules for goods.
According to London, Ms Merkel demanded a rewrite of Britain's approach to the long-vexing Irish border problem that made a compromise "essentially impossible".
The UK government also released updated preparations for a "no deal" exit at the end of the month, indicating it was increasingly expecting the outcome.
Sassoli will meet with Johnson on Tuesday evening. Johnson may have hoped that the European Union was desperate enough to avoid the damage from a no-deal Brexit that they'd glumly accept his ultimatum.
No 10 has insisted Mr Johnson will comply with the law, but Laura Kuenssberg says there are still conversations going on in Downing Street about writing a second letter, making the case that a delay is unnecessary. "His strategy from day one has been for a no-deal Brexit", said Keir Starmer, Brexit spokesman for the main opposition Labour Party.
The Commission has also rejected the accusation with spokesperson Mina Andreeva telling reporters that "under no circumstances will we accept that the European Union wants to do harm to the Good Friday Agreement".
That is something the British government says it can't accept.
"A no-deal Brexit will not be Ireland's choice and it will never be the EU's choice".
She warned that any deal was "essentially impossible" if London failed to give ground on the thorny Irish border question and keep British-run Northern Ireland in the EU customs union, the source added.
Last night the European Parliament's president said "no progress" was made during Brexit talks with Boris Johnson in Downing Street.
Donald Tusk, the European council president, tweeted directly at Johnson: "What's at stake is not winning some stupid blame game".
An earlier attempt by the government to shut down Parliament for five weeks was ruled illegal by Britain's Supreme Court because it had the effect of preventing legislators from scrutinizing the government's Brexit plans.
"The stark reality is the government put forward proposals that were created to fail", he said, adding that it was "beneath contempt" that, according to a Downing Street source reported by the Spectator, the United Kingdom could withdraw security co-operation from other European Union countries if it were forced to remain beyond 31 October. Lawmakers will return on Monday for the State Opening of Parliament, which includes a speech delivered by Queen Elizabeth II outlining the government's legislative plans.