Mr Barnier said Ireland's interest would be shared by the entire EU.
The issue of the border between the Republic of Ireland and its neighbours Northern Ireland has raised its head once again, with many pointing out that an Ireland remaining in the bloc could provide back-door access to the UK.
In the speech Barnier, who is known to be a strong opponent of any soft bargain with a Brexit UK, will signify Irish interests as "top priority" in the EU's negotiation process.
Even as Barnier offered reassurances to his audience, he underlined the challenge at hand.
The EU's Chief negotiator has warned that borders are part of managing the EU.
Barnier also discussed the border with Michele O'Neill, Irish republican party Sinn Fein's leader in Northern Ireland, in Dublin on Thursday.
Delegates from the EPP are meeting in Wicklow, south of Dublin, and Mr Barnier is expected to address their session on Friday after being given a tour of the border by Charlie Flanagan, the Irish foreign minister.
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"I want to reassure the Irish people: in this negotiation Ireland's interest will be the Union's interest".
Mr Barnier said: 'if we put things in the right order, if we negotiate with mutual respect, without any kind of aggressivity. if we are open to finding solutions, there is no reason why a strong Europe can not maintain a strong relationship with the United Kingdom'.
He said he hoped next month "as soon as possible" to find agreement on key points where the decision to leave the European Union had created "huge and serious" uncertainty.
Mr Fearon added: "The coming months are going to be critical for Ireland and the future of our economy; these talks will set in stone for many years the trading relations between and across this island".
"If we put things in the right order, if we negotiate with mutual respect without any kind of aggression ... if we are open to finding a solution, there is no reason why a strong Europe can not maintain a strong relationship with the United Kingdom", he said.
Talks on a "bold and ambitious but fair free-trade agreement" could only begin once progress has been made on issues including the UK's divorce bill.