Davis said Brussels' track record on talks meant they might only be concluded at 11:59pm on the day before Britain leaves the European Union in March 2019.
In such circumstances, lawmakers would only get to vote on the final deal after Britain had actually left the EU.
But within hours, Prime Minister Theresa May told lawmakers that she was confident a deal would be secured in time for MPs to vote before Britain leaves.
Opposition parties and anti-Brexit groups said the government was in chaos.
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"The way the union makes its decision tends to be at the 59th minute of the 11th hour," Davis told a parliamentary scrutiny committee.
"That is precisely what I would expect to happen."
"It will be a lot of pressure, very high stress, very exciting for everybody watching."
Pressed on whether that meant a vote in parliament on the deal could be after March 2019, he replied: "It could be, yes", adding: "Well, it can't come before we have the deal".
Davis's office then issued a statement appearing to row back on what he told the committee.
"We are working to reach an agreement on the final deal in good time before we leave the EU in March 2019," a spokeswoman said.
"Once the deal is agreed we will meet our long-standing commitment to a vote in both houses and we expect and intend this to be before the vote in the European Parliament and therefore before we leave."
Keir Starmer, Brexit spokesman for the main opposition Labour Party, said May and Davis had only added to the "confusion and chaos over the government's approach" to the Brexit negotiations.
"Parliament must have the final say on the terms of Britain's exit from the EU before March 2019," he insisted.
Jo Swinson, deputy leader of the opposition, anti-Brexit Liberal Democrats, said the government's handling of Brexit was descending into a farce.
"We must ensure this calamitous government cannot impose a disastrous Brexit onto the country, and that the British people have the option to reject a bad deal and stay in the EU," she said.