May was also due to meet French President Emmanuel Macron in Paris, seeking support from the bloc's powerbrokers for her request to delay Brexit for a second time.
She is hoping EU leaders will agree at an emergency summit on Wednesday to postpone Brexit from April 12th to June 30, to give her more time to get her divorce deal through parliament.
British MPs have rejected the text, and May's government is now in talks with the opposition Labour party to try to find a way through the deadlock.
But these discussions are moving slowly, and EU negotiator Michel Barnier said May must explain in Brussels what another postponement would achieve.
“The length of the extension must be linked to the purpose — what it's for — and that depends on what Mrs May will say to European leaders tomorrow,” he told reporters after a meeting of EU ministers in Luxembourg.
He added: “It is for her to bring the roadmap.”
The EU has already granted one delay — the original Brexit deadline was March 29th — and Barnier said it would not be the bloc's fault if Britain crashed out this week, risking huge economic disruption.
“No deal will never be the EU's decision, it will always be the responsibility of the United Kingdom to tell us what it wants,” he said.
EU ministers have expressed frustration at the turmoil in London, where MPs still cannot decide how to leave the EU almost three years after the referendum vote for Brexit.
“We are in a very, very frustrating situation here,” said Germany's Europe minister Michael Roth as he arrived in Luxembourg.
His French counterpart Amelie de Montchalin told reporters that “we want to understand what the UK needs this extension for”.
“And then comes the question of the conditions of what role we'd want the UK to play during this extension time,” she added.
Britain is requesting only a short delay to avoid having to take part in European Parliament elections next month, but EU leaders are expected to offer a longer postponement.
EU Council president Donald Tusk's office has floated the idea of a “flexible” extension of up to a year, with an option for London to leave earlier if it finds a way through, but there is no agreement on this.
Some in the EU are worried that during a long delay, British representatives could disrupt EU budget planning and reforms during indefinite Brexit talks.
A spokesman for May said Britain had “engaged constructively through this process and you can expect the UK to continue to do so”.
Neither May nor Merkel spoke to the media during their talks in Berlin, but the German leader has previously said she would work “until the last hour” to avoid a “no deal” Brexit.
“I will do everything in order to prevent a no-deal Brexit,” Merkel said Friday.
“Where there's a will, there's a way.”
However, Macron — who May meets in Paris on Tuesday evening — has raised the possibility of rejecting the delay request, warning he does not want to simply prolong the uncertainty.
Paralysis and disarray
The diplomatic disarray in Brussels is mirrored by political paralysis in London that has forced May to promise to resign as soon as she gets this first stage of Brexit over the line.
The weakened British leader had been hoping to come to Brussels with either her deal approved or some sort of alternative way forward drafted that could convince the likes of Macron.
But her talks with the opposition Labour Party have made no tangible progress and seem unlikely to find common ground before she flies to Brussels seeking a second delay in three weeks.
“The problem is that the government doesn't seem to be moving off the original red lines,” Labour leader Jeremy Corbyn said Monday.
The government will instead present a plan to parliament Tuesday to outline how long it intends to delay Brexit.
This is part of legislation passed into law late Monday to force May to postpone Brexit if the only other alternative is a no-deal scenario.
May's talks with Labour have stumbled over Corbyn's demand that Britain join some form of European customs arrangement once the sides formally split up.
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EU officials are ready to include such a promise in the outlines of the sides' future relationship that was agreed alongside the binding withdrawal deal.
But May knows that the prospect of close post-Brexit economic relations could further fracture her government and party ahead of possible snap elections.
Almost any form of European customs arrangement would keep Britain from striking its own global trade agreement and leave one of the biggest perceived advantages of Brexit unfulfilled.