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 Brexit deal before October 31.
However, the Irish Government has previously rejected a deadline on the backstop to avoid a hard Border.
Ms Foster told a 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," she said.
Ms Foster, whose party props-up Prime Minister 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."
Meanwhile, the UK government has repeated its intent to compete with Ireland for overseas investment by cutting company taxes once Brexit goes through.
UK Trade Minister Liz Truss has said Britain will be "more competitive" and "more confident" after it leaves the EU.
She told the Conservative Party conference in Manchester that Britain would be "a low-tax, flexible, entrepreneurial leader in the world".
Inside an austere and gloomy meeting room on the fourth floor of Ireland's EU embassy in Brussels Simon Coveney, the Tanaiste and Minister for Foreign Affairs, sat down last Friday afternoon after one of his most gruelling weeks in some time.
British prime minister Boris Johnson has been roundly criticised for his contributions to what was a pretty heated and toxic debate in the House of Commons on Wednesday. The inflammatory nature of the debate and the language used by Johnson could have significant consequences. It may not be just another day of drama and vitriol in the British parliament.
A hard Brexit could push the economy here into recession and the government may need to step in to boost the economy with extra spending, the Economic and Social Research Institute warned today.