May's office declined to comment Tuesday on what it called "alleged remarks", and said its focus was on seeking changes to her deal that Parliament would accept.
During another fractious debate in the House of Commons, the prime minister made no new concessions on policy other than to stretch the deadline for agreeing a deal until the brink of the UK's formal exit from the bloc, due on 29 March.
"The talks are at a crucial stage", May told Parliament.
Adding, "By getting the changes we need to the backstop; by protecting and enhancing workers' rights and environmental protections and by enhancing the role of parliament in the next phase of negotiations, I believe we can reach a deal that this House can support".
"Having secured an agreement with the European Union for further talks, we now need some time to complete that process", she said.
Parliament is to hold a debate on Brexit on February 14 but with just 45 days until Britain leaves the bloc it is not expected to change the course of the exit process, and no date has been set for another vote to approve or reject May's deal. She said May would bring her deal back to Parliament for a vote "as soon as the issue around the backstop has been sorted out".
The EU last week rebuffed Mrs May's efforts to renegotiate a deal that she secured previous year but was later overwhelmingly rejected by MPs.
A working group comprised of both pro and anti-Brexit Conservative MPs has been discussing possible alternatives.
Eurosceptic Conservative MPs see the backstop as a way of tying the United Kingdom to the EU's trade rules indefinitely.
She faced accusations that she's deliberately running down the clock in order to blackmail Parliament into backing her divorce package under the threat of a chaotic, no-deal split that could hit the pound by as much as 25 per cent.
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May also told MPs she rejected a proposal put forward by the main opposition Labour party for Britain to join an EU customs union.
Brexit Secretary Stephen Barclay and David Lidington, May's de facto deputy, are in Strasbourg meeting members of the European Parliament, while British Foreign Secretary Jeremy Hunt is in Paris as part of a diplomatic offensive.
Hunt said he had "open and thoughtful discussions" with French Foreign Minister Jean-Yves Le Drian.
Le Drian had a different message, tweeting that "rapid progress" was needed to ensure an orderly divorce.
May also hinted that a provision in the UK's Constitutional Reform and Governance Act, which dictates that global treaties must sit for 21 days of parliamentary sittings before they can be ratified, would be waived to give her government more time to broker an acceptable deal with the EU.
Meanwhile, students supporting a second referendum urged Corbyn to "get off the fence" on Brexit, in a stunt in his north London constituency.
Many of Labour's younger, newer supporters who propelled the veteran socialist to the party leadership want to stay in the European Union - but numerous seats Labour holds in parliament are in pro-Brexit hotbeds.
"A lot of people have noticed the complete lack of opposition on this", said Kira Millana Lewis, an 18-year-old student and Labour member. "And we can set this country on the course for the bright future that every part of this United Kingdom deserves".
The UK government has admitted that it will fail to roll over all trade treaties involving the European Union and third countries by 29 March, with global trade secretary Liam Fox confirming that negotiations with some countries have now been prioritised over others.
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