The European Union is due to lay out its Brexit strategy for the first time later, which is likely to prompt debate over the question of the Irish border.
The draft document is expected to say Northern Ireland might have to follow EU single market rules to avoid a "hard border", in lieu of other solutions.
Downing Street has dismissed any prospect of a return to a hard border.
But the DUP has said if the Irish Sea became a trade border it would withdraw its support for the UK government.
One of the party's senior members, Sir Jeffrey Donaldson, tweeted: "This fundamentally breaches the understanding reached in December and would undermine the constitutional status of NI in the Belfast Agreement.
"If the EU or Dublin believes the UK government will be signing up to a border in the Irish Sea, they are deluded. Taoiseach (the Irish prime minister) knows that."
Meanwhile, former Conservative prime minister John Major is due to give a speech on Brexit later.
He is expected to lay out his recommendations for a successful deal between the UK and the EU.
The EU commissioners' 120-page draft Brexit withdrawal document will refer to three possible options for avoiding physical infrastructure on the Irish border.
However, the only one to be fleshed out will be the government's least-favourite: the option of Northern Ireland staying aligned with European rules and regulations, says BBC Brussels reporter Adam Fleming.
The document will encapsulate - in legally binding text - agreements already reached on Ireland, citizens' rights and the UK's so-called "divorce bill".
It will form the basis of further negotiations with the UK in areas like the transition and might still be tweaked by the 27 remaining member states.
EU negotiator Michel Barnier has said the document will not contain any surprises because it translates the political pledges made by both sides in the talks so far.
According to reports by Irish broadcaster RTE, the text will say that Northern Ireland may be considered part of European Union customs territory after Brexit, alluding to a single "regulatory space" on the island of Ireland with no internal barriers.
Leaked letter
On Tuesday, a leaked letter from Boris Johnson has appeared to accept the possibility of future customs border checks on the island of Ireland after the UK leaves the EU.
In the letter, obtained by Sky News, the foreign secretary tells Theresa May 95% of traffic would still pass unchecked if there was a hard border.
