Brussels - British Prime Minister Theresa May has closed in on a divorce deal with European Union chiefs with last-minute progress on the thorny issue of the Irish border after months of deadlock.
May met European Commission chief Jean-Claude Juncker and was to see EU president Donald Tusk in Brussels for what the bloc says is the "absolute deadline" for an improved offer from London.
A deal on the key divorce issues -- Ireland, Britain's divorce bill and the rights of EU nationals in Britain -- would allow the EU to approve the start of trade and transition talks at a summit on December 15.
"Tell me why I like Mondays!," Tusk said on Twitter, saying he had been "encouraged" by a phone call with Irish Prime Minister Leo Varadkar on the negotiations.
"Getting closer to sufficient progress" at the December summit, he added.
May and Juncker did not speak to reporters as she arrived, with the pair shaking hands before the EU commission chief ushered her in to lunch by putting an arm behind her back.
Ireland's demands on the status of the border with British-ruled Northern Ireland have been the key stumbling block recently, with fears that the talks could even collapse amid tensions between the two neighbours.
But European Parliament members who met Juncker on Monday said there were signs Britain was ready to concede on keeping the EU customs and single market rules for Northern Ireland after Brexit in order to resolve the border problem.
"I was told that the UK is prepared for that, and that there is agreement there, which to be honest is a surprise to me," Philippe Lamberts, a Green MEP who is on the European Parliament's Brexit task force, told reporters.
"The pie is almost ready. If everything goes well, the lunch could be much more about the future relationship than about settling the withdrawal agreement."
- 'Critical moment' -
Ireland's state broadcaster RTE said the two sides had reached an agreement that there would be no divergence on the rules between north and south -- a key demand by Dublin -- although the language was yet to be finalised.
Varadkar -- who last week received Tusk's backing for an effective veto on a Brexit deal if Ireland was not happy -- said he would be making a statement about the first phase of talks later Monday.
In a further sign of progress, Tusk cancelled a trip to the Middle East on Tuesday and Wednesday "due to a critical moment in the Brexit talks and due to consultations on draft guidelines for the second phase" his spokesman Preben Aamann told AFP.
London has however rejected the EU's deadline and, ahead of next week's summit, appears keen to push the talks to the wire.
"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.
Luxembourg Prime Minister Xavier Bettel seemed to back Britain's position, saying that the decision was ultimately for the leaders of the remaining 27 countries.
"It seems to go into the right direction. I hope that the next hours will bring that. But it is as well not for Mr. Juncker and Mr. Barnier to decide", but for the EU summit next week, Bettel said
May, Brexit minister David Davis and the prime minister's Brexit adviser Olly Robbins are having lunch in Brussels with Juncker, EU Brexit negotiator Michel Barnier and Juncker's chief-of-staff Martin Selmayr. She will meet Tusk later.
A formal EU decision on any deal is not expected until Wednesday.
The remaining 27 EU states have demanded "sufficient progress" from Britain on the bill, citizens rights and Ireland in order to move on to talks on a post-Brexit transition period of up to two years, and on a future relationship including a trade deal.
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.
- Bill, citizens rights -
Ireland is now the key issue, especially the problem of how to keep a "soft" Irish-UK border when Britain is leaving the EU, and avoid undermining a peace deal that ended decades of sectarian conflict in Northern Ireland.
May faces pressure from Northern Irish unionists who prop up her minority Conservative government not to create a "new border" within British territory by creating special customs arrangements on the island of Ireland.
But after months of stalemate, 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 ($53-63 billion).
They appear to have reached a compromise, with London increasing its offer, but Brussels offering enough wiggle room for the British government to be able to present its own, lower figures to the public.
A deal is also close on the rights of more than three million Europeans living in Britain, although there is still disagreement over whether they would be protected by the European Court of Justice -- a red line for Brexiteers in Britain.
By Danny Kemp