Boris Johnson and European Commission President Ursula Von Der Leyen have spoken as they try to break the post-Brexit trade deal stalemate.
The leaders were called in after negotiators for the two sides said “significant divergences” remained following a week of intensive talks.
“If there is still a way, we will see,” EU negotiator Michel Barnier said.
Sticking points include fishing rights, rules on state subsidies for business and arrangements for policing any deal.
The BBC understands the call between the two leaders began at 16:30 GMT. President Von Der Leyen will make a statement shortly.
The UK left the EU on 31 January but remains under EU trading rules until a transition period ends on 31 December.
One source close to the negotiations on the UK side suggested there had been a more optimistic outlook earlier in the week but pointed to demands for EU fishing boats to have 10-year access to UK waters as one issue that derailed progress – as had been reported in the Telegraph.
BBC political editor Laura Kuenssberg said the pattern of recent UK negotiations with the EU was for victory to be snatched from the verge of defeat at the very last moment – but that one member of the government was now putting the chances of a deal at around 50-50.
She said it would be complacent to think it would all automatically fall into place after a last bit of political scrapping.
Speaking to reporters in London as he prepared to return to Brussels, Mr Barnier said: “We keep calm, as always, and if there is still a way, we will see.”
France’s Europe minister suggested his country could veto a deal if it was not satisfied. French President Emmanuel Macron has been keen to ensure the fishing industry will not lose too much access to British waters.
But Belgian MEP Philippe Lamberts said the fishing issue had been “overdone” by both the UK and France, adding: “We should cut it down to size. It should not be allowed to derail a good deal.”
Mr Lamberts said the main issues that remain were competition and governance.
He said: “These are much more important and this is a very tough nut to crack, and it will really depend on whether Boris Johnson wants to limit the economic damage caused by Brexit.”
Meanwhile, the spokesman for German Chancellor Angela Merkel said there was “always room for compromise”.
And Irish Prime Minister Micheál Martin said he “fervently hoped” a trade deal can be agreed.
Former UK Brexit Secretary David Davis told BBC Breakfast the probability of a deal was “still high” but there would be compromise on both sides and the “big decisions won’t be this afternoon between the prime minister and president of the commission but in wires running hot between Berlin and Paris and other capitals”.
He said: “My suspicion is when it gets to the end of the month there is no time to ratify… so they will have to do some sort of freeze in place of current customs arrangements to take us through the few months until everybody from the European Parliament to the Walloon parliament actually give their opinion.”