The DUP's Nigel Dodds said yesterday that he hoped the extension of UK-EU talks could lead to a tariff and quota-free trade deal.
Following talks between the Prime Minister and European Commission president Ursula von der Leyen, the negotiations will continue, with both leaders agreeing to "go the extra mile" in search of a deal.
Boris Johnson suggested there was still hope of a post-Brexit trade deal with the European Union but the two sides remained "very far apart".
But the agreement to continue talking beyond yesterday's deadline set by Mr Johnson and Mrs von der Leyen does indicate that some compromise is possible.
DUP peer Lord Dodds said he hoped the extension of talks could lead to a tariff and quota-free trade deal.
He said: "The DUP has always believed that barriers and tariffs between North/South or East/West were neither necessary nor sensible.
"If we find ourselves in a no-deal outcome between the UK and EU, as far as Northern Ireland is concerned then Northern Ireland-EU trade will continue.
"Trade between Northern Ireland to Great Britain will be unfettered, with no extra paperwork. We must ensure that Great Britain to Northern Ireland trade is tariff-free and with the minimum checks."
The prospect that many goods from Great Britain could face a tariff when entering Northern Ireland has been addressed in a trusted trader scheme.
Ulster Unionist Assembly member Roy Beggs said: "EU officials will now be sent to Northern Ireland ports to look over the shoulder of UK officials who are doing the checking at the border control posts."
He added: "That's where we have now ended up after the DUP's support for Boris Johnson's proposals last year."
Mr Johnson said the UK would not be walking away from the negotiating table and "where there is life, there is hope" but a no-deal outcome was still the most likely scenario.
He said the UK should get ready for the breakdown of talks, resulting in tariffs under World Trade Organisation (WTO) terms from January 1.
"The most likely thing now is, of course, that we have to get ready for WTO terms, Australia terms," the Prime Minister said.
Mr Johnson spoke to Mrs von der Leyen for around 20 minutes in a call described by sources as "perfectly cordial".
The pair agreed to "keep going for as long as they still think a trade deal is possible", a source said.
A joint statement issued by the two leaders said: "Our negotiating teams have been working day and night over recent days.
"And despite the exhaustion after almost a year of negotiations, despite the fact that deadlines have been missed over and over we think it is responsible at this point to go the extra mile."
Following his talks with Mrs von der Leyen the Prime Minister updated the Cabinet.
Mr Johnson then told reporters: "We're going to continue to try and we're going to try with all our hearts and be as creative as we possibly can, but what we can't do is compromise on that fundamental nature of what Brexit is all about which is us being able to control our laws, control our fisheries, it's very, very simple.
"I think our friends get it, and we remain willing to talk and will continue to do so.
"But in the meantime let's get ready for the WTO option, and that's what I told the Cabinet."
A WTO Brexit could result in tariffs and quotas being imposed on business with the EU, which is the UK's largest trading partner.
But Mr Johnson insisted the UK will do "very, very well", with WTO terms offering a "clarity and a simplicity" that has advantages.