"We can't just have continuing uncertainty and I think Parliament should be invited to say what it would agree with", Business Secretary Greg Clark told the BBC.
Earlier, it emerged Jeremy Corbyn was prepared to table a motion of no-confidence in Mrs May personally if she didn't set a date.
Although May survived as leader last week, opposition parties are calling for Labour to propose a parliamentary motion of no confidence against the government this week.
"Parliament has a democratic duty to deliver what the British people voted for", she said.
Updating MPs following a bruising European Union summit in Brussels, Mrs May will say: "Let us not break faith with the British people by trying to stage another referendum".
"And another vote which would further divide our country at the very moment we should be working to unite it".
Chris Bryant, MP for Rhondda, said he spoke to Cabinet Office Minister David Lidington about the next steps.
"The prime minister ran away from putting her deal before parliament because even her own cabinet has doubts and she herself admits parliament won't back it", he said.
He said that "I think businesses up and down the country would expect elected members to take responsibility, rather than just be critics".
On Sunday, he said in a statement it would be "the sensible thing" to allow parliament to vote on each of the forms of Brexit canvassed, including the deal May agreed with the EU.
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May accused Blair of insulting voters and trying to undermine her government by meeting officials in Brussels. "There is no deal that can meet all the promises made for it - or one that is as good as the deal we already have in the European Union".
Whilst talk of a second poll has until now remained confined to backroom discussions, the decision to delay the meaningful vote last Tuesday has emboldened its proponents, who believe that another plebiscite may be the only way out of the current deadlock.
But others within the May government are reported to be increasingly open to the idea of testing different options for Brexit by voting on them in the parliament.
But there was confusion over efforts to secure further guarantees over the controversial Northern Irish backstop measure created to prevent a hard border with Ireland. She said the vote would be held the following week.
They are urging a "managed" no deal exit - which could involve paying the European Union for a transition period and limited agreements to limits the worst effects of crashing out.
She told MPs on Monday: "Avoiding "no deal" is only possible if we can reach an agreement or if we abandon Brexit entirely".
And the chief spokesperson for the European commission, which has been leading negotiations, confirmed on Monday that "no further meetings with the United Kingdom are foreseen".
He added that talk of a second referendum was an "internal" matter for the UK.
The Labour leader said: "She has achieved nothing, the deal is unchanged and not going to change".