The Prime Minister gave the strongest hint yet that MPs could get the chance to vote on having a second EU referendum.
Theresa May has consistently said that she opposes another vote but acknowledged that it could be taken out of her hands.
She suggested there was a strong possibility that MPs will table a motion when she brings the deal back to the Commons.
The SNP leader Ian Blackford asked Mrs May if a second referendum has been offered as part of the government's negotiations with the Labour Party which are ongoing.
The Prime Minister said: "My position on a second referendum, the government's position has not changed.
"The House has rejected a second referendum two times.
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"When we come to a deal we will have to make sure that legislation goes through this House.
"Of course it may be that there are those in this House who with to press that issue as the legislation goes through.
"But my position on this has not changed."
Number 10 played down the significance of the Prime Minister's comments saying: "It is a statement of absolute fact."
As part of a series of indicative votes held on 27 April the confirmatory vote option gained the most votes (268) but it was defeated as 295 MPs opposed it.
In that vote 198 Labour MPs supported it but 27 voted against - the exact margin it lost by.
On 1 April MPs voted on the second round of indicative votes and had their say again on a second poll as part of a motion tabled by Peter Kyle which gained 280 votes but was voted down by 292.
Speaking to the Today programme on Radio 4, Mr Barclay said: “The reason we have to go back today is not because of the Prime Minister, it is because Parliament once again refused to vote for the Withdrawal Agreement.”
He added: “That is a consequence of Parliament, not the Government. The Government has agreed a deal with the EU. It is Parliament that has forced this on the Government.”
David Gauke paved the way for the PM's comments today when he said on Tuesday it was "inevitable" that MPs would table an amendment.
"I think there is a point here to distinguish between the talks with the Labour Party that are ongoing and what will inevitably happen as and when we bring a withdrawal agreement bill through the House of Commons is that somebody will bring forward an amendment on whether there should be a confirmatory referendum to the House of Commons which has already voted twice against a confirmatory referendum or second referendum."
The issue is far from straightforward for Labour with deep divisions on whether or not there should be a second vote.
A spokesman for the Labour leader told journalists: “The issue of a possible confirmatory ballot has been discussed at every session.
“But the overwhelming focus is on the substantive issues - the customs issue, single market, rights, standards and guarantees in relation to workers’ rights.”
The spokesman said the process for a referendum “has been discussed”.
Asked if that included discussing an amendment that could be put down by MPs he said: “Every aspect of the situation has been discussed.”
Shadow Chancellor John McDonnell said on Tuesday: "What we're trying to do is make sure we arrive at a deal which first of all protects jobs and the economy, we don't think Theresa May's deal does that, and we're also discussing the issue it seems apparently she's raised in cabinet as well, about the issue about going back to the people."
But sources close to the talks have told the Mirror that the issue of a second vote has not even be broached.
