Speaking to members of a think tank at Whitehall, the Brexit Secretary admitted the democratic vote to leave the EU could be ignored.
He said: “My view is that it means there is less chance of a no deal — and less chance of no Brexit.”
The PM used her official New Year message to restate her determination to deliver Brexit.
She said she would “keep up progress in 2018” on the next stage of the Brexit talks, adding: “Making a success of Brexit is crucial.”
But her message was undermined by Mr Davis’ remarks.
A source said: “For the Brexit Secretary to express the thought that the whole thing might never happen was not what I expected – even behind closed doors.
“Nor was I the only person who reacted like that. It didn’t square with the Prime Minister’s mantra of ‘Brexit means Brexit.”
Mr Davis’s spokesman insisted he backed Theresa May and that his remarks were misinterpreted.
A spokesman said: “He was simply repeating the PM’s point that the deal is good for people who supported Leave and who fear Brexit isn’t going to happen, and Remain supporters who fear no deal.”
The seminar was hosted by Mr Davis at his Whitehall department shortly before Christmas.
He invited members of leading think-tanks to discuss the Government’s success in getting an agreement with Brussels on moving to the next phase of Brexit talks.
The omission by Mr David has caused a new rift between him and Mrs May.
It comes amid a series of damaging reports in recent weeks about Mr Davis’s handling of negations with the EU.
These include claims that he has been sidelined by Number 10.
Mr Davis is accused of going back on a pledge to publish dozens of detailed reports on showing how Brexit would affect the economy and he also suggested leaving the EU could have as much impact on the UK as the 2008 credit crash.
Theresa May used her speech to dismiss claims she was losing her grip.
This is despite a series of setbacks in 2018, including failing to win a majority in a snap General Election and losing three Cabinet Ministers in a spate of scandals.
She said: “The real test is not whether challenges come; it’s how you face them, whether you allow a task to overcome you, or tackle it head-on with purpose and resolve.”
Mrs May also noted that 2018 is the 70th birthday of “our precious NHS”, defending the Conservatives’ record on the health service in the face of attacks from critics about a lack of funding.
She said: “We will continue to invest in our NHS and ensure it can deliver a world-class service now and for generations to come.”
Labour Leader Jeremy Corbyn used his New Year message to claim Labour was “staking out the new centre-ground” in politics and was a “Government in waiting”.
He said: “We are a government in waiting. The hope of a new Britain is closer than ever.
“Now the Establishment’s secret is out: they’re not as strong as they appear. Let’s face it, they have no idea how to fix their broken system or upgrade our stagnant economy.
“In 2018, Labour’s mission is to give our people support and security and use their talents, unleash their creativity and fulfil their hopes.”