EU Commission President Ursula von der Leyen announced this evening that after a brief phone call with Boris Johnson, "considerable progress" had been made on a Brexit deal.
However, the EU leader says that "big differences" that will be "very difficult to bridge" will persist as both sides are ready to get to the heart of the negotiations.
It comes after Mrs von der Leyen and Mr Johnson participated in a crunch phone call at 7pm UK time tonight.
The conversation was billed as an "inventory" rather than a moment of breakthrough or breakdown.
It did so after Michael Gove warned that the chances of the UK and EU reaching a trade deal by Sunday are "less than 50 percent".
The Minister for the Cabinet Office told Brexit Select Committee MPs that at this point, "the chances are more likely that we won't reach an agreement".
In the meantime, the heads of the European Parliament today set a deadline for this weekend for an agreement to be reached.
They warned that concluding an agreement after that date would not give MPs enough time to properly examine and then vote in favor of it before the end of the transition period “deadlock” on December 31st.
Demanding a deal by the end of Sunday will put pressure on the negotiators trying to break the impasse on crisis issues.
Michel Barnier, the EU's chief negotiator, expressed hope that an agreement was in sight this morning when he said "good progress" had been made as the talks entered the "final phase".
But he also warned that "the last stumbling blocks will remain" and that Brussels "will only sign an agreement to protect the interests and principles of the EU".
Last night, Mr Johnson told MPs that they would be called back from their Christmas break to vote for a deal, should one be made.
Boris Johnson and Ursula von der Leyen will speak by phone tonight about the state of the trade talks after Brexit
Michael Gove had previously told MPs that the chances of the UK and the EU reaching a trade deal by Sunday are "less than 50 percent".
Michel Barnier said today that "good progress" has been made in the UK-EU trade talks after Brexit
However, the EU negotiator warned that the "final stumbling blocks" still exist as the negotiations are in the "final phase".
What are the sticking points in the Brexit talks?
The UK has insisted that it regain control of its coastal waters from the end of the transition period.
However, the EU called for its fleets to maintain their previous access levels – with Emmanuel Macron under particular pressure from the French fishing industry.
First, the UK said it would reclaim 80 percent of EU quotas from January 1.
However, Brussels suggested restoring just 18 percent.
The two sides are believed to be near a "landing zone" that has a transition period of perhaps five or seven years. However, there is still no agreement.
LEVEL PLAY FIELD
The EU has insisted that the UK commit to a level playing field to ensure that businesses on the continent are not undercut by introducing lower environmental standards and regulations.
State aid has emerged as a particular problem, especially as the coronavirus is making parts of the economy unprofitable.
However, the UK says it needs to regain sovereign powers to make rules, even though it has no plans to lower standards or distort competition by subsidizing the private sector.
It seemed that this area was on the verge of being resolved before France reportedly set a number of additional conditions, including huge penalties in the form of tariffs for breaking the rules.
While the UK is happy with the "non-regression" – which means that current standards are accepted as a basis – it has rejected calls for future compliance with the bloc's rules.
Michel Barnier told EU ambassadors this week that the UK is now ready to accept the need for a "compensation mechanism" for rules that could resolve the dispute.
Getting a deal done and who decides whether to break rules has been a focus from the start.
The exemption from the European Court of Justice was one of the greatest demands made by Brexiter in the EU referendum.
But Brussels has insisted on maintaining control of governance and insisting on harsh fines and punitive tariffs for violations.
The governance problem is closely related to that of "a level playing field", with a breakthrough in the latter likely to pave the way for a breakthrough in the former.
In the past few days there has been growing optimism that the UK and the EU are not far from reaching a trade deal after months of stalemate.
But Mr Gove gave a blow to the hope that an agreement is imminent this afternoon when he told MEPs: “My new resolution, adopted a few weeks ago, is to avoid giving percentages.
& # 39; But at the moment I regretfully think that the chances are more likely that we won't reach an agreement.
"So at the moment less than 50 percent."
Mr Gove had been asked what the likelihood is that an agreement will be reached by Sunday after the group leaders in the European Parliament announced that they would at the latest accept an agreement that was to be examined and voted on.
The heads of state and government passed a statement this morning stating that they will not vote on the Brexit deal before the end of the year if they cannot access the text by the end of the weekend.
The declaration of the Conference of Presidents, initiated by Spanish member Iratxe Garcia Perez, says they are ready to hold an extraordinary meeting at the end of December if an agreement is reached by midnight on Sunday 21 December.
She also called for a draft text of the trade agreement to be made available to Members of the European Parliament as soon as possible.
Britain and Brussels remain divided on two issues: fishing rights and what is known as a "level playing field" for rules.
Progress has been made on the latter, but the dispute over future EU access to British waters threatens to torpedo talks with no breakthrough in sight.
Mr Barnier was more optimistic than expected this morning as negotiations continued in Brussels.
He tweeted: “In this final phase of the talks, transparency and unity are still important: debriefing [presidential conference of the European Parliament] this morning on negotiations.
& # 39; Good progress, but the final stumbling blocks remain. We will only sign one agreement to protect the interests and principles of the EU. & # 39;
Any agreement made by the UK and the EU must be voted on and approved by both the UK and European Parliaments before it can be implemented.
MPs are scheduled to take a Christmas break starting tonight, but Downing Street has announced that if a deal is struck, they will be called back within 48 hours.
Number 10 said: "Parliament has long shown that it can move quickly and the country would expect nothing less."
The ratification process is expected to take a few days and the negotiators are now under massive time pressure to get a deal across the line as soon as possible.
If an agreement is not agreed and ratified by the end of December, the UK and the bloc will have to act on basic World Trade Organization terms from January 1, with tariffs on goods.
Ms. von der Leyen raised hopes of a deal yesterday when she said there was a way to an agreement but warned it was "very tight".
Mr Johnson told MPs last night that they would be called back from their Christmas break to vote on a deal, should one be made
She said progress had been made on a "level playing field" for the rules, but expressed concern that the fisheries problem may never be resolved.
Speaking to the European Parliament, she said: 'From today's perspective, I cannot tell you whether there will be a deal or not, but I can tell you that there is now a way to reach an agreement.
“The path may be very narrow, but it is there and it is our responsibility to keep trying.
“The good news is that we've found a way forward on most issues, but this is now a case where we're so close and yet so far apart.
"Because two questions are still open you know them, a level playing field and fisheries."