Merkel said a breakthrough was still possible but would need "quite a bit of finesse and if we aren't successful this week, we'll just have to keep negotiating".
European Union negotiators and leaders have said they won't accept Britain cherry-picking the best parts of European Union membership and leaving the obligations or unresolved issues out of the withdrawal agreement and the country's future relations with the bloc. May's Chequers plan for a softer version of Brexit, while 63 Conservative MPs signed a letter accusing the government of misrepresenting the economic impact of a no-deal scenario.
The EU say they will continue seeking a deal until the last moment, but are concerned May could run out of time to get it through the United Kingdom parliament.
British Brexit Minister Dominic Raab will hold talks with the EU's chief negotiator on Sunday, the first in a flurry of formal meetings in Brussels where officials are trying to hammer out agreement on the terms of a divorce deal.
"With several big issues still to resolve, including the Northern Ireland backstop, it was jointly agreed that face-to-face talks were necessary", Mr Raab's office said.
Citing diplomats familiar with the situation, Bloomberg said the transition extension until the end of 2021 - which would only be enacted if trade talks slowed - would help overcome the last major hurdle in Brexit talks, namely the Irish border issue.
The key stumbling block remains the need "to avoid a hard border" between Ireland and the U.K's Northern Ireland after Brexit, he said.
German government does not expect at this week's European Union summit an agreement on "sticking points" in the Brexit negotiations, officials said on Tuesday.
The DUP is furious with plans for Northern Ireland to remain fully aligned with rules of the EU's single market after Brexit as this would create new checks on the border between Northern Ireland and the rest of the UK.
However, addressing UK MPs on Monday afternoon, the UK prime minister said that "the vast majority" of the withdrawal agreement had been concluded and that "good progress had been made on the structure and scope of the future relationship".
European Council president Donald Tusk said he had "no grounds for optimism" ahead of the meeting.
"If the European Union were not to co-operate on our future relationship, we must be able to ensure that we can not be kept in this backstop arrangement indefinitely", she said.
The head of a Northern Irish party that props up her government also raised the stakes, saying it was ready to trigger a so-called no deal Brexit to prevent what it called "the annexation" of the British province by the EU.
May's Brexit hardliner party members are also concerned about May's plans, claiming that her all-UK backstop plan needs to be clearly time limited.
He said it must be orderly for everyone, including Ireland, and a solution must be found to avoid a hard border.
DUP Brexit spokesman Sammy Wilson said "it is probably inevitable that we will end up with a no-deal scenario" because there was no agreement that would be accepted by Britain's Parliament.