She added: "The Prime Minister is a Unionist".
British Prime Minister Theresa May briefed her inner cabinet on Thursday evening that a historic Brexit deal was close, the Financial Times reported Thursday.
It would also send a message to business nervous about the process that the region remained "open for business", she added.
Eurosceptics want a time limit for how long Britain will keep following the EU's customs rules before it can strike out on its own and sign independent trade agreements with new partners.
"Trade from Great Britain into Northern Ireland would be in danger of restriction".
She said: "The uncertainty surrounding Brexit for everyone is substantial, but here in Northern Ireland it is acute".
As key Cabinet members met in Downing Street, they were warned by DUP leader Arlene Foster that they could not in "good conscience" accept the proposals now on the table from the EU.
Both sides have made positive signals in recent days though also indicated they were still short of a deal, which would define the divorce terms and include an European Union declaration stating that it would seek the closest possible ties with Britain after Brexit ranging from trade to security to research. Britain's Brexit minister, Dominic Raab, could also come to Brussels then if weekend talks cover enough ground.
The 27 states remaining in the bloc hope to announce "decisive progress" in divorce talks at an European Union summit next week and then finalise their offer of close future ties with Britain next month.
Citing figures to make its case, the report noted that the EU (together with the European Free Trade Association) accounted for 43% of Britain's services exports in 2016, worth around than £110 billion to the United Kingdom economy.
As that departure date creeps closer, pressure on May from various directions is intensifying.
It comes as Brexit negotiations enter what is being referred to as a "tunnel phase", with no publication of the British or European Union position on the backstop to be published until it is agreed.
The challenge facing the British PM now is to sell the latest formulation to the whole of her Cabinet and avoid any resignations, having already faced down the resignations of former foreign minister Boris Johnson and former Brexit minister David Davis back in July.
"But that's not a question for us, we're not members of the Conservative Party".
By withdrawing its support, the DUP could make it hard for May to pass legislation through parliament, including the budget which will be voted on later this month.
Earlier this week EU officials expected that a possible new United Kingdom proposal on the Irish border issue would suggest having the United Kingdom remain in the customs union indefinitely.
The OBR, an independent non-departmental public body, said it was "next to impossible" to predict the consequences of a no-deal Brexit.