Ireland will not re-establish borders with Northern Ireland once the U.K. leaves the European Union, the country's prime minister told CNBC, but Dublin could compete with London as a new business hub for Europe.

Taoiseach Enda Kenny, leader of the Republic of Ireland's Fine Gael party, told CNBC that he and the British Prime Minister Theresa May have agreed that there would not be a return to the borders of the past or customs posts which once separated the two states.

"We are both agreed that we will preserve the common travel area and there will not be a return to a hard border," said Kenny at the World Economic Forum on Thursday.

With the British Prime Minister soon to visit Ireland, Kenny added that the negotiations would present challenges but both leaders were resolute to achieve a mutual agreement.

Northern Ireland is a constituent of the U.K. and will leave the EU along with the rest of the U.K. The Republic of Ireland, itself a sovereign state, will remain an independent member of the EU.

As such, the country provides a competitive alternative for businesses looking to move their operations away from London, said Kenny, outlining the city's English language, "wealth of talent" and connections to both London and the rest of Europe.

"The world is shrinking in many respects and it's very important that people understand that trade is now a global issue and Ireland, as a very small country, has particular evidence of that," said Kenny.

Dublin is one of many European cities, alongside Paris, Madrid and Frankfurt, vying to attract businesses as they consider potential new headquarters outside of London.





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