The withdrawal deal, which the two sides have reached, has not yet been approved by United Kingdom lawmakers, with the Irish border backstop being the stumbling block.
Housing minister James Brokenshire said on Sunday May would commit to giving parliament another debate on Brexit with the chance to vote on alternative options, if a deal had not yet been agreed and voted upon by then.
Brexit Secretary Stephen Barclay is meeting European Union chief negotiator Michel Barnier on Monday and Foreign Secretary Jeremy Hunt will visit Paris and Warsaw for talks this week.
But in an effort to see off attempts to bind the Government's hands, Downing Street is promising another opportunity to table amendments - which are likely to include measures aimed at taking a no-deal Brexit off the table - on February 27.
Labour's Brexit policy chief Keir Starmer told the Sunday Times newspaper that his party would seek to use the debate in parliament this week to prevent May from waiting until the last minute to come back with a deal, and compel her to present a fresh accord for lawmakers to consider before February 26.
Communities Secretary James Brokenshire said: "I think that gives that sense of timetable, clarity and objective on what we are doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that Parliament very firmly has".
We are abundantly clear: Labour has to stop abdicating its responsibility, admit that Brexit will wreck the economy and jobs across the country, and respect Scotland's interest.
Tony Blair has renewed warnings that a no-deal Brexit could be "devastating" for the Northern Ireland peace process and says a second referendum could still happen.
The move is in response to fears that Mrs May is engaged in a "cynical" attempt to run down the clock before the 29 March Brexit date in order to leave MPs with a stark choice of accepting her deal or crashing out of the European Union without any agreement.
The move led to a backlash from pro-EU Labour MPs, but Mr Starmer defended the approach and warned against a split in the party.
She told Sky News' Sophy Ridge On Sunday: "I appreciate Jeremy Corbyn has come to the table but the reality is what he is proposing does not deliver on what we want as a country".
The Treasury Chief Secretary said: "As the deadline approaches, minds get focused and a deal gets done".
May will ask lawmakers on Thursday to reaffirm that they support her bid to renegotiate the backstop, a government source said.