The DUP leader has refuted reports in the Times that the party is prepared to abide by some European rules after Brexit.
The newspaper said the DUP had agreed “to shift its red lines” as part of a new deal to replace the backstop.
It added the party had said privately that it would drop its objections to regulatory checks in the Irish Sea.
Arlene Foster tweeted the “UK must leave as one nation” and “anonymous sources lead to nonsense stories”.
Mrs Foster said the party would “not support any arrangements that create a barrier to east west trade”.
When asked about the story on BBC NI’s The View, South Belfast MLA Christopher Stalford said he did not “recognise that as our party position”.
“I was at an event this evening [Thursday] before I came here, where three members of parliament were speaking and that is not the position of the party,” he said.
The backstop is the insurance policy to avoid a hard border between Northern Ireland and the Republic of Ireland after Brexit, unless and until another solution is found.
Westminster MPs rejected the backstop and withdrawal agreement negotiated by ex-PM Theresa May, which would have kept all of the UK in a “temporary customs territory” with the EU and would have seen Northern Ireland also continuing to follow other EU rules.
The Democratic Unionists (DUP) had opposed it, saying it would create a border down the Irish Sea and risk the future of the union.
On Thursday, the head of the European Parliament has said he is willing to revisit the proposal of a Northern Ireland-only backstop to break the Brexit deadlock.
But on Wednesday, Prime Minister Boris Johnson ruled out an NI-only backstop.
The UK is due to leave the EU on 31 October without a deal unless both sides can reach a compromise.