British Prime Minister Boris Johnson heads to Brussels on Wednesday for talks with European Commission President Ursula von der Leyen in a push to secure a trade deal and avoid a turbulent breakup in three weeks.
With growing fears of a chaotic no-deal finale to the five-year Brexit crisis when the United Kingdom finally leaves the European Union's orbit on December 31, the 1800 GMT meeting over dinner is cast as a chance to unlock the stalled trade talks.
A British government source said a deal may not be possible, as did EU chief Brexit negotiator Michel Barnier.
The main sticking points have been over fishing rights in British waters, ensuring fair competition for companies on either side, and ways to solve future disputes.
"There is still the chance of an agreement," German Chancellor Angela Merkel, Europe's most powerful leader, told the German parliament. "One thing is clear: the integrity of the (EU's) internal market must be preserved.
"If there are conditions from the British side which we cannot accept, we are prepared to go down a road which is without an exit agreement," she said.
Michael Gove, a senior minister in Johnson's government dealing with Brexit issues, told Times Radio the EU would have to compromise if it wanted a deal.
"The EU has to move," Gove said.
Britain formally left the EU in January, but has since been in a transition period during which it remains in the EU single market and customs union, meaning that rules on trade, travel and business have stayed the same.
That all ends on December 31, and if by then there is no agreement to protect around $1 trillion in annual trade from tariffs and quotas, businesses on both sides would be hit.
Failure to agree a deal would snarl borders, shock financial markets and sow chaos through supply chains across Europe and beyond as the world faces the economic cost of COVID-19.
A measure of expected price swings in the British pound known as overnight implied volatility jumped 25% to the highest since late March.