She'll make a statement in the House of Commons on Tuesday.
Mrs May is asking for further cross-party talks "as soon as possible".
But some MPs think she's deliberately running down the clock to try and force them into backing her deal at the last moment.
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 European Union's Brexit negotiator is urging Prime Minister Theresa May to spell out how she plans to win over Parliament less than two months before Britain leaves.
If May fails to secure any changes to the backstop the government will table an amendable motion on 26 February, she said today, with a vote the following day.
A vote on the deal is now expected to be held later this month.
Addressing the House of Commons a fortnight after MPs voted for her to go back to Brussels and replace the controversial Irish border backstop, Mrs May acknowledged that she would need "some time" to hold talks with the EU.
This week's Brexit votes may not come to much. Now the prime minister comes before the House with more excuses and more delays...
That will then be followed on Thursday by a debate and voting on a number of amendments.
"Where there's insufficient time remaining following the successful meaningful vote we will make provision in the withdrawal agreement bill, with parliament's consent, to ensure that we're able to ratify on time to guarantee our exit in an orderly way", said May.
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Media captionConfused by Brexit jargon?
Now Brexit is threatening to split his party, and many of his MPs and party members feel frustrated by his lack of clarity over the party's position on Europe.
"She is playing for time and playing with people's jobs, our economic security and the future of our industry".
This is despite Mr Corbyn repeatedly saying there should be a general election if Mrs May can not get a deal through Parliament.
Ministers are also holding talks with opposition MPs in an effort to amass a parliamentary majority for the revised agreement she is attempting to negotiate with Brussels.
Commons Leader Andrea said on BBC radio that May was not simply "running down the clock" until March 29.
In response, May claimed she addressed when the vote would be in her statement beforehand.
"We're taking back control, we won't be paying money over, free movement will end, and we will have our own independent free trade policy, so I definitely don't see the Prime Minister agreeing to Corbyn's world view".
Labour said the government was guilty of "contempt for our democracy", but Mrs May said MPs had already had days of debate to examine the Brexit deal.
International Trade Secretary, Liam Fox said in a statement: "Switzerland is one of the most valuable trading partners that we are seeking continuity for, accounting for more than 32 billion pounds worth of trade a year".
If a deal has not been agreed with Brussels then new votes on February 27 could hand power over to Parliament giving MPs a say on what happens next.
Her plan was disclosed when the former Attorney General Dominic Grieve suggested that Britain's exit would realistically have to be deferred by an extension of the Article 50 process.