She'll say that if she hasn't brought them new deal by February 27, there will then be another opportunity to vote, Communities Secretary James Brokenshire confirmed in an interview.
The British media outlets have reported that UK Secretary of State for International Trade Liam Fox was considering cutting the tariffs on imports in case of a no-deal Brexit in order to keep prices low for consumers.
Jeremy Corbyn has accused May of a "cynical" attempt to run down the clock before the March 29 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.
May has indicated, to the fury of Brexiters, that she is prepared to negotiate with Corbyn, raising their suspicions she might opt to ask the EU for Britain to remain permanently in the customs union, a deal she could get the Commons to endorse by seeking cross-party support.
In Westminster, meanwhile, May is expected to confirm she will hold another Brexit vote in parliament on 27 February.
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He said the ideas put forward by Corbyn were "not workable", because it was impossible to subscribe to his proposal to have a customs union with the EU while also influencing EU policy.
"We can't allow that to happen", Sir Keir told The Sunday Times.
But they have been working on a revised version of their bill extending article 50, which would then have to be tabled by mid-March to have a chance of passing parliament in time for exit day.
The deal replicates current trading arrangements "as far as possible", the government said when it was first revealed.
But he confirmed a meaningful vote on whether to accept or reject a revised deal might not happen until March.
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"It's this blinkered approach that's got us to where we are, with her never wanting to see where the real majority is in parliament".
But she insisted her deal already met numerous conditions he had set, without tying the United Kingdom in to a customs union arrangement which would prevent Britain from striking its own trade deals.
The prime minister is aiming to allay lawmaker concern that, unless they vote to take control of the process and order her to seek an extension of European Union negotiations, they will have lost their chance to avoid a no-deal Brexit.
May has been seeking changes to the deal with Brussels since it was rejected by a record majority in parliament on January 15.
In today's Brexit Brief, British Prime Minister Theresa May responds to the Labour party with an offer of talks, MPs gear up for a Brexit debate on Thursday and Germany experiences job losses.
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"It will be the decisions that businesses take about jobs and investment - and they will reduce them - so you have less potential to trade globally, that will mean less investment in the future and that will mean fewer jobs in the future", she told Sky News.