European Council president Donald Tusk is set to offer the UK a 12-month delay to Brexit, it is reported.
Tusk would make this a “flexible” extension that allows the UK to quit the EU before the year is up if parliament agrees a deal, according to the BBC.
However, EU leaders would need to back the plan at a summit planned for next week.
Downing Street has so far said the talks have proved “productive”.
But attorney general Geoffrey Cox told the BBC that if the pair cannot agree a Brexit deal that could pass through the Commons, an extension to Article 50 is “likely to be a long one”.
May’s own Brexit deal, which took two years to negotiate, has been rejected three times by MPs, first by a margin of 230 votes, then 149 votes and most recently by 58 votes.
Talks are set to continue today as the UK fights to avoid falling out of the EU without a deal on 12 April, its new deadline by which it must currently depart.
The UK was originally scheduled to quit the bloc on 29 March.
May is reportedly due to write Corbyn a letter formally setting out the government’s Brexit offer, as they search for a way forward.
It will include a proposal to offer MPs a vote on a confirmatory referendum next week on any Brxit deal Labour and the Tories come up with, a government source told the Guardian.
German chancellor Angela Merkel met Irish Prime Minister Leo Varadkar yesterday, and said she would do everything in her power to prevent a no-deal Brexit.
“Until the very last hour, I will say this for the German side, we will do everythig in order to prevent a no-deal Brexit - Britain crashing out of the EU - but we have to do this with Britain and with their position that they will present to us,” she said.
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“Where there’s a will there’s a way,” she added.
Varadkar called on the UK to offer a “credible and realistic way forward” to win an extension.