She told MPs that 95% of the terms of the exit had been agreed, but that the Irish border was the "considerable sticking point". "And Mr. Speaker there are some limited circumstances in which it could be argued than an extension to the implementation period might be preferable if we were certain it was only for a short time".
The government has begun formal preparations for a no-deal Brexit, publishing more than 100 technical guidance documents covering many possible impacts.
His remarks are likely to infuriate Brussels and the Irish Republic, who have both insisted that a backstop - essentially an insurance policy created to prevent a hard border on the island of Ireland in the event of a no-deal Brexit - must be part of any withdrawal agreement.
"Taking all of this together, 95 per cent of the Withdrawal Agreement and its protocols are now settled", she will say, according to excerpts from her statement to Parliament. She appears to be seeking a legal obligation on the European Union to devise a UK-wide deal that would make the toxic Brussels proposal superfluous.
May's most recent attempt to break the deadlock - her suggestion that the United Kingdom could extend the transition period "for a few months" if the United Kingdom needed more time to solve the Irish border conundrum - was met with fury by Tory MPs, who accused May of unnecessarily delaying Brexit while preparing to hand over more money to the EU.
The EU sees May's "all-UK" backstop, keeping all of Britain inside the EU customs union, as a dodge to grab unfair advantage by giving a special deal intended for a small, troubled province to Europe's third-biggest economy.
May will say that the shape of the deal across "the vast majority" of its text is now clear. Instead, May wants the European Union to let all of the United Kingdom stay in the customs area for a time.
Mrs May said neither the backstop or extended transition period could be never ending - and vowed in all circumstances Northern Ireland's business would get guarantees on full access to the United Kingdom markets.
The UK is also open to extending the transition period to allow that specific negotiation to come to fruition.
She said she wanted the option to extend transition to avoid ever using the backstop if a trade deal is close in late 2020.
Reporting from London, Al Jazeera's Nadim Baba said her position as leader of the party seemed to be in jeopardy, amid rumours of leadership challenges. "We are hearing that centrist Conservative MPs are now joining dozens of others who have sent letters to the party chair, asking them to basically trigger a leadership contest".
During a heated Cabinet meeting on Tuesday, Lidington said that he was the only person around the table who had been an MP on the fateful day in 1992, when interest rates soared in 24 hours as Britain dropped out of the European exchange rate mechanism.
"Many people say that this is just to add pressure on her not to give in to Brussels in terms of that transition period".
The Confederation of British Industry says a majority of United Kingdom firms are poised to implement their Brexit contingency plans by Christmas, steps that could include cutting jobs, adjusting supply chains outside the United Kingdom, stockpiling goods and relocating production and services overseas.