The prime minister's office said she would tell parliament that "the talks are at a crucial stage".
The EU says the backstop is vital to avoiding the return of border controls in Ireland and has refused to reopen the Brexit divorce deal, though May insists she can get legally binding changes to replace the most contentious parts of the backstop.
However, the reality is that she is using up the remaining time to try and impose a binary choice between her deal and no deal.
The government is flexible about how changes are made to the backstop, Leadsom said.
"It is the only way of giving the House of Commons the time to produce a consensus about a positive way forward if the PM can not get her deal through by mid-March".
Fair enough. What's an attempted coup in the grand scheme of things? And it is vital too that we keep pace with the best consumer safeguards and environmental protections especially in light in the biodiversity report this week.
May has also held talks with Labour, the UK's main opposition party, which said it could support a Brexit deal if the government promised to seek a close relationship with the European Union after Britain leaves.
May's deal was resoundingly rejected in December over concerns around the backstop, which MPs pointed out the United Kingdom can not exit of its own accord.
Barnier told a news conference in Luxembourg that time was "extremely short" to conclude a deal before Britain is due to leave the bloc on March 29.
The announcement came as Mrs May urged MPs to "hold their nerve" and support her efforts to secure a withdrawal deal which will deliver Brexit on time.
Massive crowds mark 40th anniversary of Iran revolution
A number of Israeli and American flags were set on fire by the crowds. The country's military also displayed missiles along rally routes.
"The Prime Minister should summon him back to London immediately to ask him exactly what is going on". Can the Prime Minister confirm that?
Just hours after her Brexit deal was decimated in the Commons, May and the Conservatives faced a confidence vote tabled by Labour leader Jeremy Corbyn.
Other MPs supporting the move include the senior Labour MP Hilary Benn, Tory former attorney general Dominic Grieve and the Liberal Democrat Norman Lamb.
Prime Minister Theresa May (back centre left) before giving a statement about progress on Brexit talks to MPs in the the House of Commons, London.
"I do not take the responsibility lightly and my government will continue its work to increase our prosperity, guarantee our safety and to strengthen our union". We can honour the result of the referendum.
And a fellow Brexiteer Kate Hoey has said that a Brexit Party could sweep the board if it was to contest an election in which Brexit was seen to have been betrayed.
Mr Barclay met a group of Tory MPs on Monday, ahead of his trip to Brussels, who are working on possible alternatives to the backstop. Are we any closer to getting rid of the backstop?
But Labour claims Mrs May is planning to delay the final, binding vote on the withdrawal deal she has agreed with the European Union until the last possible moment, so that MPs will be faced with a stark choice between her deal and no deal.
Meanwhile, Irish prime minister Leo Varadkar reportedly quashed May's hopes of renegotiating the clause over dinner in Dublin on Friday night, telling Sky News he only wanted to "restore confidence and trust" at the meeting.
Four weeks after she saw her agreement with the bloc defeated by the biggest margin in modern Parliamentary history, May will update Parliament on the progress of talks with the European Union and outline a motion she'll put before MPs for debate on Thursday, her office said.
"This week Parliament should set a clear deadline for the government to come forward with its revised deal or give MPs the chance to decide what happens next".