The jobs minister Mary Mitchell O'Connor is expected to meet officials in Brussels later to discuss the impact of Brexit.
Ms Mitchell O'Connor has said she will stress the importance of avoiding the introduction of customs or trade barriers during the discussions at the European Parliament.
The Fine Gael TD said: "It is crucial that the EU institutions at the highest levels fully appreciate the potential impacts for Ireland at the earliest stage, before any detailed negotiation process, that will prepare the terms for the UK's departure and its future relationship with the Union."
Ms Mitchell O'Connor will take part in a series of meetings with Elzbieta Bienkowska, European Commissioner for Internal Market, Industry, Entrepreneurship and SMEs, Cecelia Malmstrom, European Commissioner for Trade, and Vicky Ford, MEP, chair of the Internal Market (IMCO) Committee of the European Parliament.
She added: "(I will) emphasise the importance of the Brexit negotiations taking full account of the impact on Ireland in relation to the economic and employment context, our desire to avoid the introduction of customs or trade barriers, the competitiveness challenge, and our ability to sustain engagement in research cooperation, including under EU funding programmes."
The Common Travel Area (CTA) allows free movement of people between Ireland and the UK.
During a visit to Northern Ireland last week, Brexit minister David Davis said the UK and Republic of Ireland wanted to retain an open border.
Northern Ireland Secretary James Brokenshire has also said there is a strong will from both governments to ensure that there was no return to the borders of the past while Foreign Affairs minister Charlie Flanagan has insisted the two countries must keep the "invisible" border that exists at present after Brexit.
Meanwhile, trade and single market issues including progress on the EU-US trade negotiations (TTIP), the EU-Canada trade agreement (CETA), and the Commission's initiatives to achieve progress on strengthening Europe's Single Market will also be on the minister's agenda.
Ms Mitchell O'Connor is expected to underline Irish support for the EU's trade agenda in order to ensure that Irish exporters gain greater market share in existing markets and improved terms of entry to new markets, while urging progress on the EU's trade negotiations which have yet to be implemented (Canada) or completed (Japan and USA).