Her 27 counterparts are set to agree there has been sufficient progress on key separation issues including Britain's exit bill and the Irish border to move talks onto the future relationship.
After May addressed them over dinner in Brussels on Thursday, December 14, the leaders gave her a round of applause, while saying Britain had to spell out what it wanted quickly.
German Chancellor Angela Merkel said May had made "good offers that imply that the 27 will see sufficient progress" but added that "there remain many issues to be solved and we don't have much time".
Dutch Prime Minister Mark Rutte said May was a "formidable political operator" who should not be underestimated.
"Now two things are crucial. First is that we put the handshake of last Friday into legally binding agreements," he said.
"At the same time for the UK to come forward with their wishes their ideas on what the future relationship with the EU will be."
May sealed the divorce deal with European Commission President Jean-Claude Juncker on December 8 after all-night talks that ended months of tortuous negotiations.
It covers Britain's financial settlement, the future of the Irish border and expatriate rights, while the next stage will cover trade and a transition period to ease the break.
'Ambition and creativity'
Over dinner on the first night of the summit on Thursday night, May was "clear about wanting to move onto trade talks as quickly as possible", a British official said.
May told them she "makes no secret of wanting to move onto the next phase and to approach it with ambition and creativity", adding that the transition period was a "particular priority".
EU officials have warned it could take years after Britain leaves to formally sign a trade deal, rejecting claims by British Brexit minister David Davis that it could happen immediately afterwards.
British officials are hoping for a deal by March on a two-year transition, during which the bilateral relationship would largely stay the same, although Britain would have to follow EU laws.
A trade deal will be a tougher period, with options including following the model of a recent EU-Canada trade deal, or Norway's membership of the European Economic Area.
But questions still linger over the divorce agreement, after Davis appeared to suggest it was not legally enforceable and that Britain would only pay its exit bill if it got a trade deal.
There are particular concerns about the guarantee made by London – at Dublin's request – that there will be no frontier checks between Ireland and the British province of Northern Ireland.
EU Brexit negotiator Michel Barnier has said there will be a "separate track" in the second phase of negotiations that remains dedicated to the Irish question. – Rappler.com