"The UK would be free to leave whenever it is ready", he said.
The two leaders sat down for a working lunch, during which May "outlined the steps the government is taking to bring the Brexit process to a successful conclusion", according to a Downing Street spokesperson.
The ministers discussed the bloc's conditions for any long delay, which include Britain holding European Parliament elections in May and committing to "sincere cooperation", or not undermining the EU's important reforms and institutions should it stay a member for longer.
These would limit the power of Britain's commissioner in the European Commission, the EU's executive arm, and the role of the British prime minister at meetings of EU leaders, the aide said.
The Government earlier tabled an order enabling the elections to be held in Britain if the country has not left the European Union by the time they are due to take place on May 23.
As a last resort, May has even started cross-party talks with Labour leader Jeremy Corbyn, but there have been no results so far.
Barnier said he had no information about such a plan, and a German government spokesman said the report was "without any foundation".
But because May has already requested a delay, and with no alternative dates chosen to be voted on by lawmakers on Tuesday, the vote was not a major flashpoint in the country's long-running political crisis over how to deliver Brexit.
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The French leader has taken the lead in pushing for the bloc to be ready to show Britain the door if Westminster can not not ratify a withdrawal deal.
Prime Minister Theresa May visited Chancellor Angela Merkel Tuesday and made an evening call on French President Emmanuel Macron in Paris as she sought a further extension for Brexit beyond this Friday, April 12.
On the eve of an emergency EU summit in Brussels, chief EU Brexit negotiator Michel Barnier said the bloc was ready to grand a delay, but that the duration "has got to be in line with the objective of any such extension".
On Tuesday, members of parliament voted overwhelmingly to approve the extension request, with 420 votes in favour to 110 against.
Before May's visits to Paris and Berlin, Leadsom said she should use the meetings as an opportunity to ask European Union leaders once again to reopen the agreement.
Such an extension would mean the United Kingdom had to take part in European parliamentary elections, a prospect anathema to hardline Brexiteer Tories.
European Union envoys will hold a last preparatory meeting ahead of the Wednesday leaders' summit in Brussels at 1800 GMT on Tuesday.
May has lost the support of her Conservative party, which is split over how to exit the EU.
If a cross-party deal can not be reached, MPs are expected to vote on a series of Brexit options proposed by the government in the near future.
President Donald Trump sacks Secret Service boss Randolph Alles
A senior administration official said Trump asked for Nielsen's resignation when the two met at the White House on Sunday. CNN is reporting this afternoon that Secret Service officials found out about the director being removed... from CNN.
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