Update 1.33pm: Ireland is to bid to host two EU bodies located in London, Taoiseach Enda Kenny confirmed.
The European Medicines Agency is responsible for the protection of public and animal health through the scientific evaluation and supervision of medicines.
The European Banking Authority was tasked with finding risks and vulnerabilities in the EU banking sector at the height of the financial crisis.
Mr Kenny addressed the Dail following Michel Barnier's speech to Dublin parliamentarians.
He said: "Ireland will bid along with other countries for the two EU bodies currently located in London, the European Medicines Agency and the European Banking Authority.
"I believe that Ireland offers an excellent opportunity as a location for these."
He said Brexit was a British policy.
Update 12.40pm: The EU's chief Brexit negotiator has signalled that the peace process and Good Friday Agreement will take priority over trade and customs matters, during today's special address at Leinster House, writes Juno McEnroe.
Michel Barnier told the packed Dáil chamber that Ireland was needed as a bridge for partners across the Atlantic as well as with Britain as he praised the country's role in the European Union.
Taoiseach Enda Kenny thanked the Brexit negotiator for his contribution as well as work which has helped secure Ireland and the peace process as priorities during the exit negotiations going forward.
Mr Barnier, for his part, outlined how Ireland and the peace process would have to be addressed first by London during the fraught negotiations before the contentious issue of a future relations and even trade would then be discussed by the 27 members and Britain.
He told the joint houses of the Seanad and Dáil that trade would be an issue but nothing should come before peace on the island of Ireland.
Michel Barnier: 'I want to reassure the Irish people: in this [Brexit] negotiation Ireland's interest will be the Union's interest.' pic.twitter.com/1LO3t6jT1P— RTÉ News (@rtenews) May 11, 2017
“ We have a duty to speak the truth. The UK's departure from the EU will have consequences," he said.
"Customs controls are part of EU border management. They protect the single market. They protect our food safety and our standards.
"I already said many times: nothing in this negotiation should put peace at risk.
"This was recognised by the 27 Heads of State and Government two weeks ago. They were very clear that the Good Friday Agreement must be respected in all its dimensions.
“I also made very clear that the border issue will be one of my three priorities for the first phase of the negotiation. Together with citizens' rights and the financial settlement.
“We first must make sufficient progress on these points, before we start discussing the future of our relationship with the UK. The sooner this will happen, the better.”
Mr Kenny noted how EU leaders had recently agreed at a Brussels summit that “sufficient progress” would have to be made on three priority areas, including about Ireland, before the exit talks would be moved onto future relations between the EU and Britain.
Both Mr Kenny and Mr Barnier are set to speak at Government buildings later today.
Taoiseach Enda Kenny says he is pleased that Ireland’s specific concerns are acknowledged in the Brexit negotiating guidelines pic.twitter.com/gVThFI93uM— RTÉ News (@rtenews) May 11, 2017
Update 9.56am: The Taoiseach has warned against "verbal wars" ahead of the Brexit negotiations.
Enda Kenny is in Wicklow this morning addressing a gathering of MEPs from the EPP group.
The Chief Brexit negotiator Michel Barnier's due to address a joint session of the Dáil and Seanad this morning, before meeting the Taoiseach in Government Buildings.
Enda Kenny says the Brexit negotiations need to be conducted respectfully.
"And we believe that it's crucial that the withdrawal of the United Kingdom is managed in an orderly and competent fashion.
"We have consistently urged both sides to adopt a constructive approach to these negotiations, there is no point in having verbal wars before the negotiations ever begin," he said.
Earlier: The EU's chief Brexit negotiator arrives in Ireland today.
Michel Barnier will hold a private meeting with Enda Kenny after addressing a special joint sitting of the Dáil and Seanad.
Michel Barnier has already been in Dublin, seven months ago on a tour of European capitals.
But this two day trip is different and will include a visit to the north and the border region.
Today he is south of the border, and enjoying a rare honour in Leinster House, making a speech to a joint sitting of the Dáil and Seanad.
It is an honour previously enjoyed by Nelson Mandela, Bill Clinton and Tony Blair.
Afterwards he will hold a private meeting with the Taoiseach in Government buildings.
The goal of the two-day trip is to get a clearer vision of just how Brexit will affect Ireland, and to test the waters about how certain things might go down.