DUP leader Arlene Foster has said her party would "look at" a time-limited backstop - as she insisted there remained a chance of finding a deal before 31 October.
The proposal would put a deadline on the backstop arrangement required by the European Union to avoid a hard border in Ireland - but it has previously been rejected by the Irish Government.
Ms Foster told a Policy Exchange fringe event at the Conservative Party conference in Manchester: "In terms of the time-limited backstop, can I remind you what Leo Varadkar thinks of the time-limited backstop - he says it is not a backstop at all.
"And so in terms of the time-limited backstop we have said in the past it is something we would look at.
"I don't think it is something that Leo Varadkar would look at, but certainly if a time-limited backstop was on offer it is something that we would look at but I don't believe it is at this present moment in time."
She described the backstop proposal as "anti-democratic", but said she believed a "way forward" existed - claiming it was possible to find a deal "even at this late stage".
"I firmly believe that there is a way forward, that if the European Union and the Republic of Ireland government in particular care about protecting the Belfast Agreement as they say they are, then they need to acknowledge that the backstop will not do it for Northern Ireland or indeed the rest of the United Kingdom and therefore we need to find a new way forward."
Ms Foster, whose party props-up Boris Johnson's minority government, later added: "I think even at this late stage we can find a deal that is acceptable to the House of Commons and is acceptable to Europe."
However, she remained adamant that Northern Ireland had to "leave on the same terms as the rest of the United Kingdom" in relation to customs arrangements.
"We cannot have internal customs borders within the United Kingdom... it has constitutional implications as well as economic implications.
"Actually when you think of the amount of trade we do East-West and West-East it completely blows out of the water the North-South trade.
"I'm not saying the North-South trade is not important - it is of course important - but our East-West trade is much more important."