Northern Ireland's First Minister makes the claim on an upcoming episode of the BBC programme Hardtalk.
Arlene Foster says the UK is considering moving its border to include the Republic, as a way to 'protect the two islands against terrorism.'
Northern Ireland's First Minister was keen to stress that the government in the Republic were not yet in negotiations, but were merely discussing it with their British and Northern Irish counterparts.
She also said that the move was being discussed before the summer's Brexit vote initiated Britain's move away from the European Union.
"They were speaking about this long before the European Union exit vote was taken. How do we protect ourselves as two islands against terrorism?" she asked on the BBC show.
"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."
Foster added that she would be 'concerned' if the UK's plans for leaving the EU had been finalised, given the fact that they were still negotiating over the implications for Northern Ireland.
"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," insisted 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."
