MPs have previously rejected the idea of a second referendum in a House of Commons vote by a margin of just 12 votes.
With Tory MPs losing the whip and an appetite to stop the Prime Minister securing a deal with the EU, Saturday’s vote is now sitting on a knife edge.
Shadow Brexit minister Jenny Chapman said last night backing a vote for second referendum on Brexit would be "pragmatic" and "sensible" for Labour.
Asked what she would want to happen after a deal is passed in the Commons, she told the Andrew Neil Show on the BBC: "I would rather have a general election but we are not in control on this.
"So should that opportunity come on Saturday, to have that referendum on a deal - the deal that we don't know yet is going to be there - the pragmatic, sensible thing for the Labour party to do, given we've been asking for this, would be to take that opportunity."
A Labour Party spokesperson told Yahoo News UK: “On background, we don’t know what they are bringing back Saturday, let alone what amendments there will be.
“We’ll look at the wording of any amendments carefully but we believe any deal should be subject to a public vote.”
Mr Johnson has tweeted that a deal has been agreed, meaning a vote on it is set to go ahead on Saturday.
He wrote: “We’ve got a great new deal that takes back control — now Parliament should get Brexit done on Saturday so we can move on to other priorities like the cost of living, the NHS, violent crime and our environment #GetBrexitDone #TakeBackControl”
The news came just hours after hopes of securing any deal before Saturday were dealt a serious blow when the DUP said they could not support the proposals “as things stand”.
We’ve got a great new deal that takes back control — now Parliament should get Brexit done on Saturday so we can move on to other priorities like the cost of living, the NHS, violent crime and our environment #GetBrexitDone #TakeBackControl— Boris Johnson (@BorisJohnson) October 17, 2019
🇪🇺🤝🇬🇧 Where there is a will, there is a #deal - we have one! It’s a fair and balanced agreement for the EU and the UK and it is testament to our commitment to find solutions. I recommend that #EUCO endorses this deal. pic.twitter.com/7AfKyCZ6k9— Jean-Claude Juncker (@JunckerEU) October 17, 2019
In a statement, DUP leader Arlene Foster and deputy leader Nigel Dodds, said: "We have been involved in ongoing discussions with the Government.
"As things stand, we could not support what is being suggested on customs and consent issues, and there is a lack of clarity on VAT.
"We will continue to work with the Government to try and get a sensible deal that works for Northern Ireland and protects the economic and constitutional integrity of the United Kingdom.”
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Meanwhile, Brexit Party chairman Richard Tice MEP said he would rather have a short extension than another referendum.
He told Sky News' Kay Burley At Breakfast: "We would never support a second referendum. It would destroy trust in democracy, it would infuriate the electorate, it would be divisive, it would be ugly - under no circumstances would we support a second referendum.
"We would rather leave with a clean break on October 31.
"Faced with the alternative, we would rather (have) a very short extension so there could be a general election, and a Leave alliance could win a thumping majority and then leave on a clean-break Brexit because we would then have the numbers in the House of Commons.”
German Chancellor Angela Merkel said an agreement on Brexit is still possible but has not yet been reached.
She told the German parliament: "We're on a better path than before, but we have not yet reached the goal.”
Mr Johnson has spoken to European Commission president Jean-Claude Juncker over the phone before travelling to Brussels.
The pair are due to meet at the European Council summit, where there is hope of a Withdrawal Agreement being signed off.