European Council President Donald Tusk is proposing to make an offer of a 12-month "flexible" extension to the UK's Brexit date, the BBC reported.
The plan would let the UK leave sooner if the British parliament ratifies a deal, the BBC said, which would need to be agreed by EU leaders next week.
After her EU withdrawal deal was rejected for a third time British lawmakers, Prime Minister Theresa May invited opposition Labour leader Jeremy Corbyn for talks in parliament to try to plot a way out of the crisis.
May said earlier this week she would seek a delay that is "as short as possible" to the current Brexit date of April 12.
UK Attorney-general Geoffrey Cox told BBC that if the talks between UK's Conservative and Labour parties fail, the delay is "likely to be a long one".