Crucial negotiations to secure a post-Brexit trade deal between the UK and the EU are to resume later.
UK chief Brexit negotiator Lord Frost will meet EU counterpart Michel Barnier in Brussels to try to bridge the two sides' "significant differences".
A UK source told the BBC it could be the "final throw of the dice" to agree a deal before the end of the year.
BBC Political Correspondent Chris Mason said the mood was downbeat, but both sides still wanted a deal.
He quoted a UK government insider as saying: "Often the darkest hour comes just before dawn."
Sunday's meeting comes after talks between Prime Minister Boris Johnson and European Commission president Ursula von der Leyen failed to deliver agreement.
The pair spoke on the phone for an hour on Saturday but failed to break the deadlock on "critical issues".
In a joint statement issued afterwards they said fishing rights, competition rules and how any deal is enforced were still causing problems.
They added: "Both sides underlined that no agreement is feasible if these issues are not resolved."
However, Mr Johnson and Ms Von der Leyen said they "welcomed the fact that progress has been achieved in many areas".
Both have agreed to talk again on Monday evening.
The BBC's political editor Laura Kuenssberg said the statements signalled "clearly" that a trade deal is out of reach right now, and "if no-one budges in the next few days, it's simply not going to happen."
Areas of disagreement
Lord Frost and his team of negotiators are due to travel back to Brussels on Sunday, where they will to try and work through areas of disagreement with their EU opposite numbers.
One of these is over access to UK waters by the EU's fishing fleets.
Another is what measures there should be to ensure a "level playing field" for businesses on both sides of the Channel.
Also outstanding is any consensus on how any new agreements would be enforced, and about the role of the European Court of Justice.
If a deal is not reached, border checks and taxes will be introduced for goods travelling between the UK and the EU.
"Everyone's best interests"
The EU's chief negotiator, Michel Barnier, tweeted after Saturday's statement was published, saying: "We will see if there is a way forward."
Ireland's Taoiseach (Prime Minister) Micheal Martin also took to Twitter, welcoming the news that the teams would resume trade talks.
He said: "An agreement is in everyone's best interests. Every effort should be made to reach a deal."
Labour's shadow Cabinet Office minister Rachel Reeves said: "The British people were promised a deal and, with time running out, we urge both sides to get on with reaching an agreement."
It's not over, not yet.
The two sides in this complicated and drawn out process have agreed that it is worth trying one last time to find a way through their profound differences.
But the statements from the prime minister and the EU chief, Ursula von der Leyen, signal clearly that a trade deal is out of reach right now - spelling out that if no-one budges in the next few days, it's simply not going to happen.
A feature of Brexit negotiations has often been the last minute stand off, the political emergency, before suddenly, lo and behold, a deal emerges from the wreckage.
By Monday night, that tradition may have been proven again.
Yet it seems there is a lot more to be done than ironing out a few last minute glitches.
Even if the two sides agree a deal, there are still hurdles to overcome.
Any agreement reached will need to be turned into legal text and translated into all EU languages, then ratified by the European Parliament.
The UK government is likely to introduce legislation implementing parts of any deal reached, which MPs will be able to vote on.
And the 27 EU national parliaments could also need to ratify an agreement - depending on the actual contents of the deal.
The week to come
After the meetings between the teams on Sunday and the leaders' talk on Monday, the UK Internal Market Bill will return to the House of Commons.
Certain clauses could allow the government to break international law, by overriding elements of the original treaty with the EU for Brexit - the withdrawal agreement.
The EU are unhappy with it, as are the House of Lords, who voted to scrap those clauses of the bill.
But the government is still backing its measures, which could cause tensions in the trade talks, and they are expected to push them through the Commons on Monday night.