Boris Johnson will head to Brussels on Wednesday night for a final, face-to-face Brexit showdown.
Technical talks between the UK and EU ground to a halt this week, with "significant differences" on fisheries and EU rules.
For weeks, the two sides have been haggling over fishing rights in British waters, ensuring fair competition for companies and ways to solve future disputes.
A UK government source indicated it was unlikely a breakthrough moment was likely from the meeting itself, but could unlock issues for talks to continue.
They said: "It’s clear that some political impetus will be required for the talks to make any more progress.
"If we can make progress at a political level it may allow [Chief UK negotiator] Lord Frost and his team to resume negotiations over the coming days.
"But we must be realistic that an agreement may not be possible as we will not compromise on reclaiming UK sovereignty."
Mr Johnson has said trade talks with the bloc were proving "very tricky" and that it was "very, very difficult" to make progress, but that he was hopeful about reaching a deal.
Mr Johnson said he hoped the "power of sweet reason" would triumph but Brussels had to accept there were limits to what terms the UK would be prepared to accept.
Confirming the PM's travel plans, the PM's official spokesman said: "The PM will travel to Brussels for dinner with Ursula von der Leyen to continue discussions on the future relationship between the UK and the EU."
Mr Johnson today said he has to be "optimistic" but "it's looking very, very difficult at the moment".
Asked if Brexit talks would continue right up until the wire, the PM told reporters: "Of course, we’re always hopeful.
"But there may come a moment where we have to acknowledge it’s time to draw stumps and that’s just the way it is.”
The PM he once again trumpeted the possibility of no-deal Brexit - the so-called 'Australian' option - despite his own Budget watchdog warning it could cut 2% from GDP and delay coronavirus recovery by almost a year.
He said: "We will do our level best, but I would just say to everybody: be in good cheer, there are great options ahead for our country on any view.
"But the key thing is on January 1, whatever happens, there is going to be change."
The Prime Minister is correct that Brexit will cause more bureaucracy for firms because Britain is leaving the EU single market.
But without a trade deal, tariffs will be slapped on hundreds of billions of pounds a year in trade overnight from January 1. That could cause major delays at ports and push food prices up in supermarkets.
Sources on both sides have warned time is ticking after months of talks reached no resolution.
Despite agreeing to extend talks, and rumours of an EU climbdown on fishing, a UK government source told all political journalists last night: "Talks are in the same position now as they were on Friday.
"We have made no tangible progress. It’s clear this must now continue politically.
"Whilst we do not consider this process to be closed, things are looking very tricky and there’s every chance we are not going to get there.”
Mr Johnson said today on a hospital visit: "We will see where we get to in the course of the next two days.
"But I think the UK Government's position is that we are willing to engage at any level, political or otherwise, we are willing to try anything.
"But there are just limits beyond which no sensible, independent government or country could go and people have got to understand that."
The pound and the FTSE 100 share index have both fallen as fears mount in the City of a no-deal Brexit.
