Finance Minister Michael Noonan believes there would no need for a land border in the North if the UK leaves the European Union.
However, he said that it is vital not to have a barrier to trade with the North.
He was speaking after a Cabinet meeting where Taoiseach Enda Kenny briefed his colleagues before travelling to a major EU summit on a so-called 'Brexit'.
Minister Noonan said that Ireland and the UK have legal agreements from before the founding of the EU, which would remain in place.
"Since 1922, there has been a single labour market between Ireland and the UK, and obviously you can't have a single labour market without free movement of people," he said.
"So that's enshrined in law prior to our entry into the European Union, and that would remain the position."