The European Union says their working lunch in Brussels is the "absolute deadline" for progress on separation issues, or else it will be unable to approve the opening of talks on a future trade relationship at a summit on December 15.
Reaching agreement today will be "difficult but doable", a senior EU diplomat told AFP, with divisions remaining on the fate of the Irish border and the rights of European citizens living in Britain.
"With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December Council," a British government spokesman said in a statement.
Talks continued over the weekend, May's Downing Street office said.
May, Brexit minister David Davis and the prime minister's Brexit adviser Olly Robbins will have lunch in Brussels at 1215 GMT with Juncker, EU Brexit negotiator Michel Barnier and Juncker's chief of staff Martin Selmayr.
The British prime minister will also meet European Council President Donald Tusk, who is in charge of summits, Downing Street said.
The EU has demanded "sufficient progress" on the key divorce issues of Britain's Brexit bill, citizens rights, and Ireland in order to move on to talks on a post-Brexit transition period and future relations.
Failure to do so this month could make the EU "rethink" whether an overall Brexit withdrawal deal is possible at all, Tusk has warned, raising the prospect of a chaotic exit with far-reaching economic effects.
After months of deadlock, London and Brussels have effectively reached a deal on the contentious issue of the divorce bill, reported to be between 45 and 55 billion euros (USD 53-63 billion).
"If the UK offer is unacceptable for Ireland, it will also be unacceptable for the EU," Tusk said after meeting Irish Prime Minister Leo Varadkar in Dublin on Friday.
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