(BBC) -- Theresa May is to travel to Brussels later for a dinner with EU leaders in a bid to end a stalemate over Brexit.
The meeting, with chief negotiator Michel Barnier and Commission chief Jean-Claude Juncker, comes days after the pair said talks were in "deadlock".
Brexit Secretary David Davis will join Mrs May for the meeting, ahead of this week's summit of EU leaders.
On Sunday, the PM phoned German chancellor Angela Merkel in a further attempt to break the impasse.
Downing Street said Mrs May and Mrs Merkel agreed on the "importance of continued constructive progress" in the UK's exit negotiations in the early morning phone call.
Although Mrs May's trip was not made public during last week's negotiations, Downing Street sources insisted it had "been in the diary for weeks".
Over dinner, the PM hopes to end a stalemate over the three initial topics for negotiation - which are the amount the UK owes the EU when it leaves, the future rights of EU citizens in the UK and UK citizens living in the EU, and what happens on the Northern Ireland border.
The EU side says that until "sufficient progress" is made on these three items they will not begin discussing the UK's post-Brexit relations - on things like trade and defence - with the EU.
BBC assistant political editor Norman Smith said the negotiations were entering a "critical phase", with the possibility of the UK leaving without a deal in place becoming the "new front line" in the debate about Brexit.
The UK is doing contingency planning for such an outcome, which both sides say they want to avoid.
Conservative John Redwood predicted that "at the 11th hour" the EU would want to reach a free trade deal with the UK.
"But if we look as if we are weak, it's going to delay getting any sensible offer out of them," the former minister who campaigned for Brexit, added.
Mr Redwood said the UK would "do just fine" if no deal was reached and that he was "fairly relaxed" about the prospect of the EU imposing tariffs on UK goods, because the UK could trade "perfectly successfully" on World Trade Organisation terms.
Mrs May hopes when EU leaders meet on Thursday and Friday, they will give Mr Barnier a mandate to start talks on future trade.
But Mr Barnier, speaking after the fifth round of trade talks in Brussels, said there was no agreement on how much the UK should pay the EU when it leaves.
He said: "On this question we have reached a state of deadlock which is very disturbing for thousands of project promoters in Europe and it's disturbing also for taxpayers."
Mr Juncker added that the Brexit process would take "longer than we initially thought", blaming delays on the UK's failure to settle its financial obligations.
Last week an internal draft document suggested the EU was going to begin preparing for the possibility of trade talks beginning in December - provided the UK does more to bridge the gap on the key negotiating points.