European Council chief Donald Tusk is to propose EU leaders agree to offer the UK a year-long "flexible" Brexit extension of Article 50 beyond April 12 until March 31, 2020.
Britain will have the option of leaving the EU earlier if the UK parliament ratifies the EU Withdrawal Agreement – but could remain for another 361 days.
It comes as May has penned her own letter to Tusk asking for a shorter extension until June 30.
The Prime Minister proposed the delay as she tries to find consensus to pass a divorce deal through the House of Commons.
May has this week been courting Jeremy Corbyn and the Labour Party after MPs have repeatedly failed to agree on how Britian should exit the EU.
The UK is still set to leave the EU on April 12 – two weeks later than the original withdrawal date – and remains set to crash out without a deal.
'BREXTENSION': Theresa May is set to be offered a deal to delay Brexit unil March 31, 2020 (Pic: EPA)
In her letter to Tusk, May said: "It is frustrating that we have not yet brought this process to a successful and orderly conclusion.
"The United Kingdom Government remains strongly committed to doing so, and will continue to act as a constructive and responsible Member State of the European Union in accordance with the duty of sincere cooperation throughout this unique period."
Mrs May said if ongoing talks with Labour do not lead to a "single unified approach soon" then the Government would instead look to establish a "consensus" on options on a future relationship that could be put to the Commons.
She added: "The Government stands ready to abide by the decision of the House, if the Opposition will commit to doing the same."
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POWERBROKER: Jeremy Corbyn may make-or-break Theresa May's deal on Brexit (Pic: EPA)
“It is frustrating that we have not yet brought this process to a successful and orderly conclusion.”
Top-level talks aimed at finding a way out of the Brexit deadlock will continue between the Government and Labour on Friday.
The discussions are taking place as May faces an upcoming week of hectic diplomacy as she battles to keep her EU withdrawal agenda on track.
As Government talks with Labour on EU withdrawal went into another day, the issue of a new Brexit referendum continued to be a focus of attention.
Ministers have considered the possibility of giving MPs a vote on holding a referendum on a deal as part of the talks with Labour, the Daily Telegraph reported.
It is understood the Government could set out proposals to Labour leader Jeremy Corbyn in a letter on Friday.
FURY: Britain remains bitterly divided over Brexit since the referendum in June, 2016 (Pic: EPA)
Talks between the Government and Labour lasted four-and-a-half hours on Thursday.
David Lidington, effectively the deputy prime minister, led the Government's negotiating team with Brexit Secretary Steve Barclay, Chief Whip Julian Smith, Business Secretary Greg Clark and Theresa May's chief of staff Gavin Barwell.
On the other side of the table were shadow Brexit secretary Sir Keir Starmer and shadow business secretary Rebecca Long-Bailey along with senior Labour officials.
Labour's victor with a reduced majority and vote share in the Newport West by-election, Ruth Jones, said she is against a no-deal exit from the EU.
LAST GASP: Theresa May will be hoping for a deal with the EU before April 12 (Pic: PA)
May faced a continued challenge to her authority from Parliament as the House of Lords debated a Bill aimed at extending the Brexit process in a bid to avoid a no-deal scenario.
The remaining stages of the European Union Withdrawal (No.5) Bill will be considered by peers on Monday, threatening a new political headache for Read More – Source