Mr Green is a former First Secretary of State under Theresa May and appeared on the flagship programme to talk about the Government’s policy towards Northern Ireland.
While he said the Government had “no intention” of introducing a border, Newsnight presenter Evan Davies asked Mr Green if the PM was “bluffing” when she told Eurosceptics within her Party there will be another border poll if they pursue too hard a Brexit.
The MP said: “No she is certainly not bluffing.
“Almost equally important is the practicality of it.
“I think a lot of this border dispute, whether it’s Ireland or other parts of the UK you have to look at the practicalities.
“We now know there are more roads that cross the Irish border than there are in the Eastern border of the European Union and every other country on that eastern border.
“The idea that you can have a traditional border there would not only be political nonsense, it makes no sense in practical terms.”
Mr Davis said Mr Green was telling Eurosceptics to compromise more and they feel Brexit is “on the line”.
He added: “It’s not going to be a proper Brexit if all of the ideas are implemented.”
But Mr Green replied: “I’m not just telling Brexiteers to compromise, I’m telling everyone to compromise.
“I’m telling everyone to be practical, to stop getting in ideological camps and say ‘what we all want is for Britain’s trade to flow as freely as possible’.”
Jacob Rees-Mogg had told Theresa May he had “no doubt” the UK would “win” any hypothetical Irish border referendum before comparing it with the 2015 Scottish independence vote.
But Mrs May quickly “slapped down” the Tory MP, sources have revealed, telling him in no uncertain terms the two situations are not comparable and the UK “cannot be confident” at holding the six counties.
The campaign for the reunification of Ireland has grown since the Brexit vote, with Northern Ireland voting heavily to Remain in the European Union.
And with the 100th anniversary of the 1921 partition of Ireland approaching, support for a border poll will only increase in the coming months and years – especially as the Brexit process continues.