British Prime Minister Theresa May closed in on a divorce deal with European Union chiefs yesterday 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 yesterday 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.