Northern Ireland First Minister Arlene Foster has said the UK is developing a proposal that would see the UK border moving to include the Republic.
In an upcoming interview with the BBC programme Hardtalk, talking about the possibility of such a move, the Democratic Unionist Party leader said: "They were speaking about this long before the European Union exit vote was taken. How do we protect ourselves as two islands against terrorism?
"How do we protect ourselves in other ways? And the way they were talking about was using the common travel area and having that special relationship recognised by working very closely together.
"Of course this will have to be accepted by the other member states in Europe.
"We can't enter into negotiations into any of this until Article 50 is triggered and the Republic's Government is very keen to point out that they are not in negotiation at the moment they are in discussion."
Yesterday, Ms Foster told Stormont Assembly members she would not expect or want the UK government to adopt a position until all the options - including implications for Northern Ireland - had been considered.
She said she would be "concerned" if plans for exiting the EU had been finalised.
"It should be no surprise to anyone that the UK has not yet finalised its plans for leaving the EU, indeed if they had I would be concerned, given that they are in detailed discussions with us to help shape the plan," said Ms Foster.
"They are still at the information-gathering and analysis stage which is a huge task covering many areas of government.
"We are currently feeding our own assessment of the issues into this process through the Joint Ministerial Committee and extensive bi-lateral engagement between officials."