Merkel, the bloc's most powerful leader, emphasised she did not want this, saying: "I want very clearly a deal and not some unpredictable solution, on this we are working very intensively".
"It is a hard negotiation, we are aware of it, everyone must show good will", commented the Belgian Prime Minister on his arrival on the second day of the summit, which could partly be seen in the light of the state of progress of negotiations between EU-27 and UK.
EU President Donald Tusk said reports the talks were in deadlock were "exaggerated", hailing a speech May made in Florence, Italy, last month for breaking the impasse.
The Prime Minister arrived at the European Union headquarters this afternoon with a tough challenge of convincing leaders talks are ready to move on to the trade and future relationship phase.
Luxembourg Prime Minister Xavier Bettel warned: "We are not going to delay the bill indefinitely".
Mrs May made her remarks after leaving a European Council breakfast in Brussels.
The European Council in Brussels decided that insufficient progress had so far been made in divorce talks to move on to trade discussions now, as Britain had hoped.
Reflecting those concerns, Lithuanian President Dalia Grybauskaite, said that "we all not only the United Kingdom but us also, (must) go for real negotiations and not just negotiating in the media by rhetoric".
An EU source said that starting preparations on guidelines for the trade talks would save time if and when the political decision was taken to move forward in December. Those include the exact sum of Britain's divorce bill which the European Union estimates at 60-100 billion euros ($70-120 billion), compared with a possible 20 billion euro offer from London the rights of citizens affected by Brexit, and the status of the Northern Ireland-Ireland border.
And a French presidency source said "scoping work has already broadly started", referring to preparations on the broad areas a deal might cover. "From my side there are no indications at all that we won't succeed", she said.
"We must work together to get to a result that we can stand behind and that works for all of our people", she said.
Dutch Prime Minister Mark Rutte said May "pleaded her case well", but called for more "concrete" positions in the run-up to the December meeting.
"The full and final settlement will come as part of the final agreement that we're getting in relation to the future partnership", she told reporters on Friday.