Next week, the EU's leaders will meet at a summit to discuss the extension of Britain's membership after 29 March, as well as the terms and length of the delay.
It has previously voted against the deal over concerns around the Northern Ireland backstop.
Meanwhile, there were reports that ongoing talks with the Northern Irish Democratic Unionist Party (DUP) will see its 10 MPs switch to backing the deal.
Following a vote by MPs to allow an extension to Article 50, the European Council president Donald Tusk met Dutch Prime Minister Mark Rutte in The Hague on Friday, ahead of talks with Angela Merkel and Emmanuel Macron on Monday.
The United Kingdom's divorce from the European Union has sown chaos throughout May's premiership and the Brexit finale is still uncertain. But the Commons is voting now on a more damaging plan to seize control of the Commons agenda next week with the aim of taking over the Brexit process. This supposed vote to eliminate No Deal/WTO rules, the Remainer preference, contained a curious appeasement to Brexiteers and the European Research Group (ERG) to keep No Deal on the table, but at the same time directed MPs to extinguish the No Deal option.
North West Leicestershire MP Andrew Bridgen said: "Obviously colleagues can switch if they want to but I am pretty sure we have the numbers to stop the deal".
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Meanwhile Europe's leaders are considering whether to agree to the UK Parliament's call for Brexit to be delayed.
May planned to spend the next few days trying to persuade opponents in her Conservative Party and its parliamentary allies to support the withdrawal agreement, which Parliament has resoundingly defeated twice.
The changes would address the DUP's concerns over the backstop - an insurance policy aimed at avoiding controls on the sensitive border between the British province of Northern Ireland and European Union member Ireland.
Former cabinet minister Esther McVey, who resigned over the Brexit deal, suggested she and other MPs could now back it, even though it was "rubbish".
But if the Commons has not passed a resolution approving the negotiated withdrawal agreement by March 20, then the motion said it is "highly likely" the European Council would require a "clear goal for any extension" and to determine its length.
The first would be to get the a deal on the Withdrawal Agreement and then have a short extension while the second would be a longer period to sort out Brexit, he explained. We recognise there is a range of opinions on when to press the case for the public being given the final say, which means some of these MPs will vote for the Wollaston amendment, some may vote against and some will abstain. So, Parliament is faced with the same old unacceptable deal in MV3 this week.