MPs will be called to Parliament for a special Saturday sitting in a decisive day for the future of Brexit.
Parliament will meet on 19 October after a crunch EU summit - seen as the last chance for the UK and EU to agree a deal ahead of 31 October deadline.
If a deal is agreed, Boris Johnson will ask MPs to approve it - but if not, a range of options could be presented.
The BBC's Laura Kuenssberg says these could include leaving without a deal, and halting Brexit altogether.
MPs will have to agree a business motion in the Commons for the sitting to take place.
Assuming they do, the additional day would coincide with an anti-Brexit march run by the People's Vote campaign, which could see thousands of protesters heading to Westminster.
The House of Commons has only sat on four Saturdays since 1939, including on 2 September that year, due to the outbreak of World War Two.
The last time there was a Saturday sitting was 3 April 1982, due to the invasion of the Falkland Islands.
The prime minister has said he is determined the UK will leave the EU on 31 October, despite legislation, known as the Benn Act, which requires him to write to Brussels requesting a further delay if a deal is not signed off by Parliament by 19 October - or unless MPs agree to a no-deal Brexit.
Scottish judges said on Wednesday they would not rule on a legal challenge from campaigners seeking to force the PM to send the letter - or to allow an official to send it on his behalf if he refused. They said they would delay the decision until the political debate had "played out".
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.
Labour leader Jeremy Corbyn said his MPs would "do everything we can in Parliament, including legislating if necessary, to ensure [Mr Johnson] makes that application".
"The idea that the prime minister will defy the law yet again is something that needs to be borne in mind," he added, appearing to reference the unlawful suspension of Parliament last month.
But former Conservative MP Dominic Grieve, who now sits as an independent after rebelling over Brexit, said he was a "bit mystified" at the need for a one-off Saturday sitting.
"I realise we are in the middle of a political crisis, but it is not a political crisis which makes me think we could not be sitting on the day before or on the following Monday," he told BBC Radio 4's World at One. "The government simply has not explained itself."
Talks are ongoing between the UK and EU after Mr Johnson submitted new proposals for a Brexit deal, centred on replacing the Irish backstop - the policy negotiated between Theresa May and the EU to prevent a hard border returning to the island of Ireland.
However, the EU has said there would have to be "fundamental changes" to the ideas put forward in order for them to be acceptable.
For example, Irish Taoiseach (Prime Minister) Leo Varadkar told the Dail (Parliament) on Wednesday the UK's proposal to take Northern Ireland out of the EU customs union was a "grave difficulty" for his government.
Mr Varadkar and Mr Johnson are expected to meet for further talks later this week, but after the two leaders spoke on the phone for 45 minutes on Tuesday night, the Irish PM told broadcaster RTE he believed it would be "very difficult" to reach an agreement before the end of the month.
The UK's chief negotiator, David Frost, will meet European Commission officials later - but sources on both sides told BBC Brussels reporter Adam Fleming that technical talks had effectively reached the limit of what they could achieve.
However, Home Secretary Priti Patel said the government had been putting in "very intense" work in recent weeks to get a deal, so "nothing is over".
While getting an agreement was still their preference, they were "absolutely clear" that the UK would leave the EU on 31 October "come what may", she added.
Brexit Secretary Steve Barclay and the EU's chief negotiator, Michel Barnier will also have a lunch meeting on Thursday to discuss the state of play.
As the clock ticks down towards the summit, the political tension has been rising.
A row broke out on Tuesday after a No 10 source said a call between Mr Johnson and the German chancellor, Angela Merkel, had made a deal "essentially impossible", claiming she made clear a deal based on his proposals was "overwhelmingly unlikely".
Mrs Merkel's office said it would not comment on "private" conversations.
But the President of the European Council Donald Tusk sent a public tweet to Mr Johnson, accusing him of playing a "stupid blame game" - a criticism echoed by a number of opposition parties in the UK.
Meanwhile, the UK has been told it will still be liable to pay into the EU budget until the end of next year, even if it leaves without a deal this month.
The budget commissioner, Gunther Oettinger, said the UK was fully signed up for the whole of 2020 - the last year's of the bloc's current financial framework.
"If the British are not prepared to pay, we are sure we will get the money at a later stage but not immediately," he said.
This special sitting will be a huge day.
That is because it will be the moment when Boris Johnson either returns to chants of "hail the conquering hero" - if he manages to get this elusive Brexit deal - or, more likely, returns with no-deal and has to set out his next steps.
And we are hearing that No 10 may seek to seize the initiative by putting down a series of motions for MPs to vote on - in other words asking them do they want to leave with no deal, do they want to revoke Article 50, etc.
But at the same time that Boris Johnson wants to use that moment to try and grasp the initiative, it is clear the rebel alliance of opposition MPs also wants to seize the day.
They want to ensure Boris Johnson sits down, gets out the Basildon Bond and writes that letter to the European Commission asking for a further delay.
So both sides are now poised to try and gain control of that Saturday to map out the next steps, assuming - and I think it is a fairly widespread assumption in Westminster now - that there is not going to be a deal.