Talks are stalled on the question of how to avoid a policed frontier between Northern Ireland and the Republic of Ireland, without erecting new barriers between Northern Ireland and the rest of Britain.
"In those circumstances, there would be no need for any proposal of this sort and I'm clear that I expect the implementation period to end at the end of December 2020".
"It was mentioned - both sides mentioned the idea of an extension of a transition period as one possibility that is one the table and would be looked into", European Parliament president Antonio Tajani said, according to the Independent UK.
The EU is considering allowing Britain to leave the EU over a longer period in return for agreeing to prevent a hard border on the island of Ireland.
Eurosceptics in May's Conservative Party are likely to accuse her of delaying Brexit, and will balk at the prospect of Britain continuing to pay about 10 billion euros (S$15.8 billion) a year into the EU's budget.
U.K. Prime Minister Theresa May said she is weighing a plan that would keep the U.K. bound to European rules for longer, in an attempt to break the deadlock in talks.
Barnier said "we need time, we need much more time" for talks as he arrived to brief leaders, vowing to work "calmly and patiently" for a deal in the coming weeks.
"There is a message of goodwill, readiness to reach an agreement".
Merkel said: "The chance of achieving a good and sustainable withdrawal agreement in good time is still there, and it is really in the interest of our relations with Britain, in the interest of our economy. and of course in the interest of people in our countries".More news: Dragonfly: Sundar Pichai publicly addresses Google’s plans to return to China
And one person familiar with the discussions said May's Tory party would find it hard to be fighting the next general election - due in 2022 - while the country is still inside the single market and customs union.
Anthony Wells, director of political research for YouGov, told the Evening Standard: "The slow trend of public opinion moving against Brexit we've seen over the a year ago appears to be continuing".
In other news, the Daily Mirror carries an interview with the mother of poisoned former spy Sergei Skripal, who says she fears she will never see her son again.
On Thursday afternoon, European Union leaders, Switzerland and Norway were due to meet with 21 Asian leaders including Chinese Prime Minister Li Keqiang, to promote ties between the two regions.
Ms May had lost her Conservative Party's majority in last year's election and risks a damaging defeat that could trigger a leadership contest, a so-called no-deal Brexit and even a new election.
British Prime Minister Theresa May had earlier addressed her fellow leaders, indicating that she could accept extending the post-Brexit transition phase to take the heat out the deadlocked issue of the Irish border.
"They want it to be temporary, to be replaced by something better".
Britain says it has not asked for an extension, but May has not yet come up with proposals for unblocking the border logjam.
Davis previously led Britain's negotiations to leave the European Union but quit his role as Brexit Secretary in July previous year.
May urged both parties to show "courage, trust and leadership", but came to Brussels without the concrete new proposals the European Union has asked for. Others at the bar managed to capture videos of the four leaders enjoying themselves and, naturally, posted them online.