The Secretary of State for Northern Ireland James Brokenshire has said it would be impossible for Northern Ireland to remain inside the EU single market and customs union while the rest of the UK was outside.
Mr Brokenshire said however that there were already "subtle distinctions" between agricultural regulation in Northern Ireland and in Britain which may facilitate, in the future, the all-island approach to the regulation of agri-food production as a way to avoid a hard border.
Speaking in Brussels, the Mr Brokenshire said: "I find it difficult to imagine how Northern Ireland could somehow remain in [the customs union and single market] while the rest of the country leaves. I would find it impossible.
"But as we have made equally clear we are determined to find bespoke solutions to Northern Ireland's unique circumstances, not least as the only part of the UK to share a land border with an EU member state."
However, the Secretary of State suggested there may be flexibility in the agri-food sector.
"There are slightly, subtly different standards across the whole of the UK, and [that is] why Northern Ireland and Ireland are aligned as a separate unit as contrasted with Great Britain," he said.
Mr Brokenshire cited the Foot and Mouth outbreak in 2001 as an example of where the island of Ireland was treated separately from Britain (England, Scotland and Wales).
"When we had Foot and Mouth and the outbreak there in Great Britain we were able to maintain that separation between livestock in Northern Ireland as contrasted with all the challenges we were experiencing in Great Britain."
Speaking at the European Policy Centre (EPC), following separate meetings with the EU Agriculture Commissioner Phil Hogan and the Chief Negotiator Michel Barnier, Mr Brokenshire said: "We believe this is something that is doable in terms of maintaining standards, and having that approach on the island of Ireland that reflects the real life aspects of this, without creating barriers east-west in terms of the internal UK market."
The Secretary of State referred to the UK's position paper on Northern Ireland published in August which stated: "It is important to note that north-south cooperation on agriculture has enabled the island of Ireland to be treated in policy and operational terms as a single epidemiological unit for the purposes of animal health and welfare."
He said: "It is something we remain firmly open minded about to ensure we prevent a hard border from emerging, and I think it is this comprehensive approach that will be needed, looking at customs, looking at regulatory issues, and looking at how you deal with enforcement smartly, that really does provide the answers and solutions that we believe are out there, that can be created to ensure we don't see a hard border."
Mr Brokenshire suggested that as competences were returned from the EU to the UK, some could be devolved to UK regions, including Northern Ireland, and that this could facilitate the handling of agri-food regulation on a more all-island basis.
However, he stressed that no solution would be permitted that required checks between Northern Ireland and Great Britain.
He said: "We've said we want to be open minded about this, that we don't want to create any new barriers east-west between Northern Ireland and Great Britain.
"We think we can do that in an overall integrated way that ensures that there aren't those frictions that emerge east-west or indeed north-south around the agricultural industry."