Enda Kenny says "a stream" of British banks and financial firms have enquired about moving to Ireland.
The Taoiseach says Ireland will compete fairly but firmly to attract business here after Brexit.
He was speaking during an interview with Bloomberg TV in New York, where he again predicted Brexit would take longer than two years to negotiate.
However, he said that Ireland is already poised to benefit from firms looking to stay within the EU.
"In every political issue like this there are always opportunities," he explained. "We're having a stream now of enquiries from Britain about the possibility of financial houses, banks or others moving to different locations.
"Ireland will compete fairly and hard with other countries," he added. "Obviously we offer a particular range of attractiveness as an English-speaking country in the Eurozone, one hour away from London."
On the subject of freedom of movement, the Taoiseach argued "one of the fundamental principles of participating in the European Union is that if you want access to the most developed market on the planet - that is the single market - then you must cater for those freedoms.
"One of those is freedom of people. There will be no concession given by Europe in that regard."
He also suggested that "all of the comments and speculation and rumours that are made are only that" and negotiations will only begin in earnest once Article 50 has been triggered by the British government early next year.
He stated it would be "impossible" to guess what the eventual date of Britain leaving the EU before, and reiterated that Ireland has a contingency plan for Brexit.
