Senior negotiator Olly Robbins was reported to have been overheard in a Brussels bar saying that Theresa May planned to wait until the end of March before confronting MPs with a choice between her deal or a lengthy delay to Brexit.
But Mr Barclay insisted that it remained “the agreed position of the Cabinet” to work to secure a favourable deal but plan for the possibility of no-deal.
Asked whether Mr Robbins’s reported comments reflected Government policy, the Brexit Secretary told BBC Radio 4’s Today programme: “No. The Prime Minister has been very clear that we are committed to leaving on March 29.”
Mrs May is facing a potential confrontation with Eurosceptic Conservatives, who have warned they will not back a motion she has tabled for debate on Thursday, which they believe effectively endorses a policy of ruling out no-deal.
The motion asks the Commons to reaffirm its decisions in an earlier debate on January 29, when amendments were passed requiring the PM to go back to Brussels to replace the controversial Irish backstop, but also rejecting a no-deal outcome.
One member of the Leave-backing backbench European Research Group (ERG) told the BrexitCentral website: “We told the Government very clearly last night that we will not support this motion and in fact we urged them, indeed pleaded with them at senior level, to withdraw it yesterday - but they took absolutely no notice. Frankly, we despair.”
Meanwhile shadow Brexit secretary Sir Keir Starmer said Labour is committed to preventing Mrs May from pursuing a “reckless” policy of running down the clock to the point where MPs may be faced with a choice between her deal or no-deal with just days to go to the March 29 deadline.
Labour has tabled an amendment for debate in the Commons on Thursday which would require the Government to either put her deal to a vote by February 27 or allow Parliament to take control of the process.
Sir Keir, who is due to meet Mr Barclay on Wednesday, said Labour will also support a proposal from backbencher Yvette Cooper, which has the backing of senior Tories including former party chairman Dame Caroline Spelman and ex-minister Sir Oliver Letwin.
Ms Cooper’s amendment would require a vote by the middle of March on delaying Brexit, unless Mrs May secures Parliament’s support for either her deal or a no-deal withdrawal by that time.
Sir Keir told Today that Labour “will support that”, but sidestepped the question of whether frontbenchers who vote against it or abstain would lose their jobs.
Several shadow ministers were allowed to stay in post despite disobeying orders to back an earlier amendment from Ms Cooper last month.
“I’m clear what my job is on this, and that is to get amendments down that stop the Prime Minister doing what she’s doing, because it is actually a reckless policy,” said Sir Keir.
“What the Prime Minister is up to is obvious. She’s coming to Parliament every other week, pretending there’s progress and trying to buy another two weeks, edging her way towards March 21, when the next EU summit is, to try to put her deal up against no-deal in those final few weeks.
“Parliament needs to say ‘That’s not on’.”
Downing Street declined to comment on reports of the remarks supposedly made by Mr Robbins to colleagues in a Brussels hotel bar.
ITV News said the official who heads the UK’s negotiation team was heard saying that if MPs do not vote for a deal, the EU would probably grant an extension to the two-year Article 50 withdrawal process, but it would be “a long one”.
He was quoted as saying: “The issue is whether Brussels is clear on the terms of extension. In the end they will probably just give us an extension.
“Got to make them believe that the week beginning end of March... Extension is possible but if they don’t vote for the deal then the extension is a long one...”
Conservative party vice-chairman Chris Philp later dismissed the report, telling BBC’s Newsnight: “What a civil servant might speculate in a bar after a few drinks is frankly not that important.”
However the comments reinforced suspicions among MPs that Mrs May is trying to “run down the clock” in an attempt to force them to back her agreement.
Tory Brexiteer Andrea Jenkyns tweeted: “If true, the PM should stop ignoring the wishes of the British people and disregarding her own red lines.”
Former Ukip leader Nigel Farage said Mr Robbins was part of the “civil Service fifth column” and called for him to be sacked for his combination of “treachery and incompetence”.
However ERG deputy chairman Steve Baker said it is the view of the Prime Minister which counts.
“Officials advise. Ministers decide. If the PM decides we are leaving on March 29, deal or no deal, that will happen,” he said.
Meanwhile, it has been reported that MI6 chief Alex Younger is expected to stay on beyond his retirement date to guide the secret intelligence service through Brexit.
Downing Street declined to be drawn on a report that officials want Mr Younger, 55, who is due to retire in November, to carry on for 12 months to two years after Britain has leaves the EU.