She is expected to ask parliament to reaffirm its support for her plan to try and renegotiate the part of the deal relating to the future of the Ireland-Northern Ireland border.
Opponents of the government accuse May of deliberately wasting time so that Parliament will face a last-minute choice between her deal and no deal.
As the clock ticks down to Britain's scheduled exit on March 29, May is trying to persuade the European Union to change a deal that was agreed between London and Brussels late previous year but overwhelmingly rejected by parliament in January.
Justice Minister Rory Stewart told the BBC on Monday that differences between the two aren't as great as some suggest, but the government can't accept a customs union that would prevent Britain from negotiating trade deals with other countries. On Thursday MPs will get another chance to "take control" of the Brexit process.
She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so.
"No one could responsibly propose this [a no-deal Brexit]".
"If the meaningful vote has not happened, so in other words things have not concluded, then parliament would have that further opportunity [to vote] by no later than February 27", he said.
Should the parliament give May more time on Thursday, it would mark the second extension since her Brexit deal was defeated by MPs in January.
He acknowledged that more work was needed to get the United Kingdom ready for Brexit on March 29, telling the BBC's Andrew Marr Show there are "still steps that are currently being put in place" but "there is steady work that is going on, 10,000 civil servants that are now focused on this" and the Border Force was "ramping up" its staff.
We must therefore continue to prepare for the worst-case scenario, which is what a no-deal Brexit would represent.
But in the case of a "no-deal" Brexit, those agreements will no longer apply to Swiss-British relations, and the new bilateral trade agreement between the two countries will kick in.
The head of business lobby group the Confederation of British Industry warned that the chances of Britain leaving the European Union next month without a deal have increased and the country has now entered "the emergency zone".