Boris Johnson will fly to Brussels later for talks on a post-Brexit deal with the European Commission President Ursula von der Leyen.
Time is running out to reach a deal before 31 December, when the UK stops following EU trading rules.
The pair will hold talks over dinner, after negotiations between officials ended in deadlock.
Major disagreements remain on fishing rights, business competition rules and how a deal will be policed.
At the dinner, Prime Minister Johnson will work through a list of the major sticking points with Mrs von der Leyen, who is representing the leaders of the 27 EU nations.
A UK government source said progress at a political level may allow the negotiations – between the UK’s Lord Frost and EU’s Michel Barnier – to resume over the coming days.
But the source added that it was important to be “realistic” that an agreement might not be possible.
EU sources told the BBC that Mr Barnier briefed the bloc’s Europe ministers that talks were tilting towards no deal being reached before the deadline.
Cabinet Office minister Michael Gove said “there needed to be movement from both sides” but added that the UK wanted to be “in control of its own rules and regulations”.
He also said that: “Often, around the table when you have two political principles one-on-one you can often find a way through.”
Mr Johnson will take part in Prime Minister’s Questions before travelling to the Belgian capital. EU leaders are due to meet for a summit of their own on Thursday.