He likened the border question to solving the issue of "IRA killing people on our streets"
A DUP MP has suggested Dublin could become a border for EU citizens travelling to Northern Ireland.
Jeffrey Donaldson says passports of people travelling to the UK from France are currently checked in France, before people enter Britain.
He told the Pat Kenny Show here on Newstalk: "Is there any reason why we couldn't have the same, a similar arrangement in Dublin?".
Host Jonathan Healy pointed out that Dublin authorities could not stop every person travelling through Ireland, to ask them if they were going up to Northern Ireland.
Mr Donaldson replied: "Why couldn't they ask them that question?".
"We've solved many, many issues before - we've solved the IRA killing people on our streets - are you seriously suggesting we're incapable of coming up with a pragmatic solution to this issue? I don't believe that's the case," he added.
He also believes travel arrangements already in place between Ireland and the UK would be best kept in place.
While Sinn Féin TD and spokesperson on finance, Pearse Doherty, said there will have to be border changes.
"There is no doubt about it - it's not just in relation to whether there's a hard border or a soft border - the border will change," he said.
"We're looking at other European jurisdictions which have tariffs in place, which have borders in place; and then the question is will all of these small border roads that were opened during the peace process will they be closed again."
"The answer to that question is none of us know," he added.
It comes as Taoiseach Enda Kenny is meeting British Prime Minister Theresa May in London over Brexit concerns.
While yesterday, Mrs May said any talks on leaving the European Union must take into account Northern Ireland's land border with the south.
"We've had a common travel area between the United Kingdom and the Republic of Ireland many years before either country was a member of the European Union - nobody wants to return to the borders of the past" she said.
"What we do want to do is to find a way through this that is going to work (and) deliver a practical solution for everybody."