The two leaders will also discuss issues such as trade, tourism and a planned meeting of EU leaders in Malta
The Taoiseach is travelling to Madrid this morning to meet with Spanish Prime Minister Mariano Rajoy.
The Irish government says it is the first opportunity for Enda Kenny to have 'detailed discussions' on Brexit with the Spanish leader since the formation of Mr Rajoy's new government last October.
It is said to part of a programme of 'intensified engagement' with EU partners ahead of the start of formal negotiations between Britain and the EU.
The two leaders will also discuss issues such as trade, tourism and a planned meeting of EU leaders in Malta early next month.
Speaking ahead of the trip, Enda Kenny said: ‘We see our future very much at the heart of Europe and this view is supported by the vast majority of the Irish population.
"I look forward to exchanging views with Prime Minister Rajoy about the upcoming Brexit negotiations, in which Ireland will play a full and constructive role as part of the EU team."
The Taoiseach will also meet with members of the Irish-Spanish business community during his trip, and is scheduled to visit Primark's flagship Spanish store in Madrid.