The minister told policy wonks in a pre-Christmas seminar that the government's success in getting negotiations onto the second phase, in which trade and transition can be discussed, meant "there is less chance of no deal – and less chance of no Brexit."
According to the Mail on Sunday, the remarks were interpreted by some attendees as implying there was still a chance that Brexit might not happen - although the government has played his comments down.
But Remainers including Liberal Democrat leader Vince Cable have seized on Davis' remarks as proof that the process could yet be reversed.
Cable said: "It is striking that when David Davis' defences are down, he will admit that no Brexit remains a distinct possibility.
"His refreshing intellectual honesty shows we can still protect jobs and living standards by offering people the choice of an Exit from Brexit.
"This admission will give hope to millions of people as we enter the new year.
"As David Davis himself once said, if a democracy cannot change its mind, it ceases to be a democracy."