The leaders are expected to announce on Thursday whether or not they will hold a special summit in November to finalise a Brexit deal.
However, European Council president Donald Tusk has warned that without new "concrete proposals" from the British to break the logjam over the Irish border backstop, further progress on a deal may be impossible.
Expectations were low before this week's summit in Brussels, once dubbed a "moment of truth" for Brexit, after a breakdown in talks between the lead negotiators at the weekend.
"Today there will be no breakthrough", said Lithuanian President Dalia Grybauskaite.
The so-called "backstop" will apply if there is no proper EU-UK trade deal post Brexit.
The summit also was meant to lay the groundwork for an additional planning meeting next month for the U.K.'s exit - though, as the BBC writes, it's possible that European Union leaders will formally say they are going to use the November gathering to prepare for that no-deal scenario.
May's allies, the Northern Irish Democratic Union Party (DUP), has threatened to vote against a planned British budget if May agrees to something with the EU that would create more differences and barriers to the existing ones between Northern Ireland and the rest of the UK. The EU says a time limit would defeat the point of the backstop.
Calming voice: EU Brexit negotiator Michel Barnier says work continues.
EU Trade Commissioner Cecilia Malmstrom noted Wednesday that "the United Kingdom can not negotiate any trade agreement as long as they are a member of the European Union".
At a three-hour cabinet meeting on Tuesday morning, which included ministers with reservations about her strategy, May said a deal was possible if they all stood together.
Michel Barnier said ‘we need more time’ to reach a deal
Tajani, however, also emphasised that "without an agreement on the three points (EU citzens rights in the UK, Brexit divorce bill and the Northern Ireland matter), the European Parliament can not and will not vote in favour of the agreement".
Britain's Prime Minister Theresa May leaves 10 Downing Street in London, Britain, October 17, 2018.
But a longer transition would not necessarily resolve the backstop issue, which must be included in the withdrawal treaty and ratified before the end of March to avoid the damaging "no deal" scenario.
It was a gruelling House of Commons experience for May, who was grilled by all sides of the Brexit argument and reminded of how many factions she must please to have a chance of getting a Brexit deal through Parliament.
"We do not know what they want, they do not know themselves what they really want - that's the problem", she said.
Many suspect that will not be enough time, which has led the European Union to demand a "backstop" to ensure there are no customs posts or other controls along the now invisible border between Northern Ireland and Ireland.
Malmstrom said the Europeans "see this merely as preparations being made by the U.S.to negotiate with them and others".
But both London and Brussels have pledged to avoid any physical infrastructure, or "hard border", anxious that it could upset the delicate peace process that ended decades of violence between Protestant supporters of British rule over the province, and Irish Catholics nationalists, who believe in a united Ireland.
Last weekend intensive negotiations failed to produce a Brexit deal, as European Union officials believe May has as yet been unable to agree politically to a possible customs arrangement, called backstop, after Brexit on the Irish border.
Repeatedly she failed to answer the hard questions on Brexit, on Chequers and on any divorce bill the United Kingdom might have to pay. Brexit must be orderly for everyone and for all the issues including the island of Ireland.