European Council President Donald Tusk is proposing to offer the UK a 12-month “flexible” extension to its Brexit date, according to a senior EU source.
His plan, which would need to be agreed by EU leaders at a summit next week, would allow the UK to leave sooner if Parliament ratifies a deal.
The UK’s Conservatives and Labour Party are set to continue Brexit talks later.
Theresa May will write to Mr Tusk with the UK’s request for a further delay to Brexit, it is understood.
The UK is due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by MPs.
Downing Street said “technical” talks between Labour and the Conservatives on Thursday had been “productive” and would continue on Friday.
Attorney General Geoffrey Cox has told the BBC that if they fail, the delay is “likely to be a long one”.
Prime Minister Theresa May has said a further postponement to the Brexit date is needed if the UK is to avoid leaving the EU without a deal, a scenario both EU leaders and many British MPs believe would create problems for businesses and cause difficulties at ports.
On Wednesday, MPs voted – by a majority of one – in favour of a backbench bill which would force Mrs May to ask the EU for a further extension.
However, the PM wants to keep any delay as short as possible.
To do that, she and Labour leader Jeremy Corbyn would need to agree a proposal for MPs to vote on before 10 April, when EU leaders are expected to consider any extension request at an emergency summit.
If they cannot, Mrs May has said a number of options would be put to MPs “to determine which course to pursue”.
Mr Cox told the BBC’s Political Thinking podcast that particular scenario would involve accepting whatever postponement the EU offered, which was likely to be “longer than just a few weeks or months”.
But Conservative Brexiteer Sir Bernard Jenkin said the EU was “toying” with the UK and the PM was under no obligation to accept the terms of any extension, even if mandated to by MPs.
“The government just wants cover,” he told BBC Radio 4’s Today. “They want an excuse to do what they are going to do anyway, which is to take us into some kind of extension. The British people don’t want that.”
But he said an extension of a year or so would be better than leaving on the terms agreed by the PM, accusing her of being “pretty dishonest” about her willingness to countenance a no-deal exit.
Europe’s leaders have been split over whether, and how, to grant any extension.
However, BBC Europe editor Mr Ben Rory has been told by a senior EU official that Mr Tusk “believes he’s come up with an answer”, after several hours of meetings in preparation for the summit.
President of the European Council Donald Tusk thinks he may have found a solution. Though it doesn’t exactly roll off the tongue.
He’s proposing what he calls a “flextension” which could see the UK signing up to a one-year-long Brexit delay with the option to cut it short as soon as Parliament ratified the Brexit deal.
Mr Tusk believes the arrangement would suit the EU and the UK – and as one EU official put it to me: it would avoid Brussels potentially being faced with “endless” UK requests for repeated short extensions every few weeks.
EU leaders will discuss Mr Tusk’s proposal at their emergency Brexit summit next Wednesday. By law, their decision must be unanimous.
The leader of Germany’s ruling Christian Democrat Union party, Annegret Kramp-Karrenbauer, suggested something else the EU could do: take another look at the controversial backstop guarantee to keep the border open after Brexit.
Far from official EU Brexit policy, but it gives us a taster of the kind of conversations going on behind closed EU political doors.
The EU has previously said that the UK must decide by 12 April whether it will stand candidates in May’s European Parliamentary elections, or else the option of a long extension to Brexit would become impossible.
Talks between Conservative ministers and Labour lasted nearly five hours on Thursday.
Mr Corbyn has written to his MPs saying discussions included customs arrangements, single market alignment, internal security, the need for legal underpinning to any agreements and a “confirmatory” vote.
The main item of business in the last frantic 24 hours has been the cross-party talks between the Conservatives and the Labour Party.
From both sides, it sounds like they are serious and genuine, and negotiators got into the guts of both their positions and technical details on Thursday.
Remember, behind the scenes there isn’t as much difference between the two sides’ versions of Brexit as the hue and cry of Parliament implies.
But the political, not the policy, distance between the two is plainly enormous.
Shadow Treasury minister Clive Lewis told the BBC the party would not be talking to the government if a “confirmatory referendum” was not an option.
But 25 Labour MPs – including a number representing Leave-voting seats – have written to Mr Corbyn, saying another referendum should not be included in any compromise Brexit deal.
Asked whether another referendum on any final deal was a credible option, Mr Cox said: “A good deal of persuasion might be needed to satisfy the government that a second referendum would be appropriate. But of course we will consider any suggestion that’s made.”
If the talks fail, the government faces an additional obstacle in the form of a backbench bill which would force the PM to seek a new delay.
Passed by MPs by one vote on Wednesday, the bill is being scrutinised by the House of Lords, who will next consider the draft legislation on Monday.
Ministers have argued it could increase “the risk of an accidental no-deal” in the event the EU agreed to an extension but argued for a different date than one specified by MPs.
That would mean Mrs May having to bring the issue back to the Commons on 11 April, when European leaders would have returned home, the prime minister’s spokesman said.
After a meeting with Irish Prime Minister Leo Varadkar in Dublin, German Chancellor Angela Merkel said her country still hoped for an “orderly Brexit”.
“We will do everything in order to prevent… Britain crashing out of the European Union,” she said.
“But we have to do this together with Britain and with their position that they will present to us.”