If this represents a new established position, then it means a deal is essentially impossible not just now but ever.
It comes shortly after German Chancellor Angela Merkel told the Prime Minister in a call on Tuesday that the prospect of agreeing a deal is now "overwhelmingly unlikely". The chancellor's spokesman declined to comment on "confidential conversations".
The source also said there were "all sorts of ways" they could scupper the Benn Act, which requires Mr Johnson to seek a fresh Brexit extension if he cannot get an agreement by October 19.
Varadkar said it would be "very hard to secure an agreement by next week".
Bank of England warned despite preparations, no-deal Brexit will hit United Kingdom households hard. "And, of course, it isn't really", said the Irish leader.
But should a delay still be granted at the European Union summit, Johnson will campaign for a "no-deal" in any snap election, the Downing Street source told The Spectator.
Sassoli will meet with Johnson on Tuesday evening.
The Taoiseach said the United Kingdom had reneged on commitments made to Northern Ireland and then "put half of that back on the deal and said that's a concession, which it isn't really".
Johnson spoke to German Chancellor Angela Merkel as he tried to salvage new divorce terms he has proposed ahead of next week's pivotal European Union summit in Brussels.
She added that a deal would not work unless Northern Ireland remained in a customs union with the EU, which has seen talks become dangerously close to breaking down.
The BBC's Europe editor Katya Adler said it was "no secret" Berlin found the UK's proposed new customs solution for Northern Ireland problematic.
They said: 'We will make clear privately and publicly that countries which oppose delay will go to the front of the queue for future cooperation. "The EU is not interested in a negotiated outcome at this time".
The official Leave.EU Twitter page quoted Mr Banks, adding: "'We're sorry".
Keir Starmer, Brexit spokesman for the main opposition Labour Party, described the reported suggestions that Brexit negotiation talks have stalled as "sabotage" by Number 10.
Riding a wave of British frustrations with the saga, Mr Johnson is threatening to leave at any cost - with or without a withdrawal deal - on October 31.
Sterling fell against all of its major counterparts yesterday as investors saw these latest developments as lowering the chance of a deal being struck for an orderly Brexit.
According to London, Merkel demanded a rewrite of Britain's approach to the long-vexing Irish border problem that made a compromise "essentially impossible".
The government is planning to hold a special Saturday session of parliament on October 19, the day after the European Union summit, whether or note there is a deal.
Meanwhile, at the Court of Buckingham Palace, Queen Elizabeth II signed an order suspending the British parliament at the end of Tuesday's business. 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. The speech will then be debated by MPs throughout the week.
Strategists disagree on what impact a further extension to the Brexit deadline would have on foreign-exchange markets.
The Prime Minister must have found a deal by the end of October 17/18 to avoid a dilemma over the Benn Act, which compels him to ask Brussels for an extension if he can not get an agreement past MPs when he returns, a move he has ruled out taking.