Other parties - the SNP, Lib Dems, Plaid Cymru and Greens have called on Mr Corbyn to push for a no-confidence vote against the government as a whole.
But it's not clear when the vote will happen - nearly certainly not this year - or what impact it would have if passed.
The Labour leader told the House of Commons he was bringing forward the action immediately after Theresa May said she planned to allow MPs to vote on her withdrawal agreement in January.
Mr Corbyn told the Commons the motion would be tabled "immediately", and would read: "This House has no confidence in the Prime Minister due to her failure to allow the House of Commons to have a meaningful vote straight away on the Withdrawal Agreement and framework for future relationships between the United Kingdom and European Union". That is why MPs want to be able to vote against it. It would mean Parliament doesn't have confidence in her.
Earlier, she had accused Labour of "acceding" to the government's timetable and "allowing them to waste another month". That's not what this is.
It would, however, be embarrassing for the Prime Minister who has only just won another no confidence vote from within her own party.
Defence Secretary Gavin Williamson, Home Secretary Sajid Javid and Treasury Chief Secretary Liz Truss are pushing Mrs May to step up talks with the European Union in the hope of securing a concession that will satisfy the Democratic Unionist Party, which props up the minority Tory Government.
She said it would do "irreparable damage" to the integrity of British politics.
Mr Barclay said planning for a no-deal Brexit needs to be "much more of a priority for businesses up and down the country".
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May accused Blair of insulting voters and trying to undermine her government by meeting officials in Brussels.
"I have listened very carefully to what members on all sides of the House have said and it's very clear that it is that is very bad, unacceptable, to be waiting nearly a month before we have a vote on the crucial issue facing the future of this country".
Earlier on Monday, an European Union spokesman said it had provided the "clarifications" requested on the contentious issue of the Northern Ireland border backstop and "no further meetings were foreseen".
But the Scottish National Party's Ian Blackford said the government was a "laughing stock" and Parliament needed to "take control of the situation and find a solution", insisting "let us have this meaningful vote this week".
May was asked if it would be wiser to seek an extension of the Brexit deadline rather than leaving with no deal on March 29 when the Article 50 process runs out of time.
"I lost the vote last week - and if you lose, that is ultimately conclusive", he told Sky News. "What Parliament will be faced with is a decision to exercise its responsibility to deliver the referendum result, to deliver Brexit".
"I know this is not everyone's flawless deal".
But what it suggests is that despite widespread frustration on all sides, Jeremy Corbyn is so far stopping short of taking a real shot at toppling May's administration, and is unlikely to do so unless, and until, he thinks he can win.
In the Commons yesterday, Mrs May gave her strongest warning yet about the potential impact of a no-deal Brexit, saying it would "risk the jobs, services and security of the people we serve". "Do not imagine that if we vote this down, a different deal is going to miraculously appear".