Following the crushing defeat last week of her agreement with Brussels, the Prime Minister will make oral and written statements to the House explaining how she intends to proceed.
She will also table a “neutral” motion to be debated and voted on - along with any amendments tabled by MPs - on January 29. Neutral motions are usually unamendable, but in this instance MPs will be able to express an alternative to the Government’s plan.
Government sources said she would be holding further talks with MPs, as well as business leaders and trade unionists, throughout the week in an attempt to find a way forward.
But after she briefed the Cabinet in a conference call on Sunday about her first round of cross-party contacts last week, there was little expectation she was ready to offer concessions that could win over opposition MPs.
Instead reports suggested she was preparing to press for changes to the Northern Ireland backstop in the hope she can win round Tory Brexiteers and her allies in the DUP who voted against her original deal.
The Daily Telegraph reported she was even considering trying to amend the Good Friday Agreement - although the paper quoted senior sources as saying the idea was a “non-starter”.
Irish foreign minister Simon Coveney was adamant over the weekend the backstop - intended to ensure there is no hard border between Northern Ireland and the Republic - was an essential part of the Withdrawal Agreement.
However there were signs some Brexiteers could reluctantly back Mrs May’s deal amid concerns a cross-party grouping of MPs are plotting to impose a “softer” Brexit - or derail it altogether.
Writing in The Mail on Sunday, leading Tory Brexiteer Jacob Rees-Mogg said: “Even Mrs May’s deal would be better than not leaving at all.”
There was anger among pro-Leave MPs at moves to enable backbenchers to take control of the Commons business from the Government - in breach of normal conventions - through a series of amendments to the neutral motion.
One group including senior Labour MP Yvette Cooper and Tory former minister Nick Boles is seeking to give time for a bill to suspend the Article 50 withdrawal process if there is no new deal with Brussels by the end of February.
Ms Cooper told BBC Radio 4’s Today programme that she believed the Prime Minister was hoping Parliament would rule out no deal on her behalf.
She said: “I think she (Mrs May) knows that she should rule out no deal in the national interest because it would be so damaging. She’s refusing to do so and I think she’s hoping that Parliament will do this for her - that is not leadership.”
It came as Business Minister Richard Harrington warned that crashing out of the EU without a deal would be an “absolute disaster” as he urged Mrs May to rule out a no-deal Brexit.
“I’ve seen what may well happen with this cut-off date. Crashing out, in my view ... is an absolute disaster - it’s not a road to a free trade agreement, it’s not a road to anything. It’s an absolute disaster for the country and it’s supported by a minority of a minority of people,” he told Today.
“She (Mrs May) should, in my view, say ‘We are responsible people, we’re going to do our duty to business, and we’re going to rule out a no deal because we want a great deal’.”
Another more radical amendment drawn up by former attorney general Dominic Grieve would allow a motion by a minority of 300 MPs - from at least five parties and including 10 Tories - to be debated as the first item of Commons business the next day.
Mr Grieve said it would enable the Commons to stage a series of “indicative votes” on the various alternatives, such as a “soft” Norway-style deal or a second referendum to establish which could command a majority.
He denied claims he was seeking to prevent Britain leaving the EU after International Trade Secretary Liam Fox accused pro-Remain MPs of trying to “hijack” the 2016 referendum vote.
Meanwhile, Sir Stephen Laws, a senior research fellow at the Policy Exchange and a former government law chief, said MPs seeking to delay or stop Brexit could risk involving the Queen.
Mrs May is expected to use her statement to explain how she intends to proceed in the run up to the vote on January 29, rather than setting out a detailed “plan B”.
Labour leader Jeremy Corbyn hit out at the Prime Minister for stymieing attempts to find a cross-party consensus through her refusal to rule out a no-deal Brexit.
“May’s no-deal threat is empty and hugely expensive, wasting billions of pounds we should be spending on vital public services,” he said.
“It’s a pointless and damaging attempt to appease a faction in her own party when she now needs to reach out to overcome this crisis.
“If the Prime Minister is serious about finding a solution that can command support in Parliament and bring our country together, she must listen to the majority of MPs, as well as members of her own cabinet, and take no-deal off the table.”
The SNP’s Westminster leader Ian Blackford MP said: “Rather than listening to other options the Prime Minister is instead closing them down, intent on cutting off any alternatives and leaving a false choice between her defeated dead deal and a disastrous no-deal.”
“It would be the height of irresponsibility and economic self-harm if Theresa May does not categorically rule out a no-deal Brexit today. Her attempt to run down the clock must be stopped.”