Finance Minister Michael Noonan has said he is confident both Britain and the EU are "in the space" to negotiate an "invisible Border" with the North.
Mr Noonan said this Border would be one that was "controlled electronically", adding the Government had not been given any reason to believe the Brexit negotiations would fail to deliver an "all-island agreement".
Mr Noonan also said he believed the negotiations surrounding Britain's EU exit will take "longer than two years" and there would need to be a "transitional period" to get both parties to a point where they could agree to a new treaty relationship.
He made the remarks just hours after British Prime Minister Theresa May announced she will begin the process of formally withdrawing Britain from the EU next week.
In a letter to the European Council, Mrs May confirmed she will trigger Article 50 of the EU treaties on Wednesday, March 29 - setting in train a two-year negotiation process.
If such a timeframe prevails, Britain will leave the EU on March 29, 2019. As sterling dipped following the news, Mrs May promised she would "negotiate hard" for the best deal for the UK.
"I am very clear that I want to ensure we get the best possible deal for the United Kingdom that works for everyone across the United Kingdom and all parts of the UK when we enter these negotiations."
But speaking in Brussels, Mr Noonan said there were "differences of opinion" in relation to Britain's desire to negotiate both a divorce and a trade agreement simultaneously.
But he insisted Ireland was both "ready and anxious" to enter negotiations. Mr Noonan said Ireland had "a number of issues" on its priority list, including the peace process in Northern Ireland and the Border, as well as trade.
"It's in our interests that we would come as close to the UK having a free trade agreement with the European Union as is possible because €1.2bn worth of trade crosses the Irish Sea every week, and it supports 400,000 jobs - 200,000 in each jurisdiction," he said.
"We've had informal discussions with the UK and we've had informal discussions with [EU chief negotiator] Mr Barnier, and both are in the space of negotiating an invisible Border, a Border which, you know, in so far as it will be controlled at all will be controlled electronically. So we see the negotiation as working out the ways and means towards achieving that set of objectives.
"We haven't so far envisaged the difficulty with either the UK or the Europeans in giving us the kind of all-island arrangement that we want."