Mr Cook is travelling to Cork to open an extension
The Taoiseach Leo Varadkar has held a meeting with the CEO of Apple, Tim Cook.
The two men met at Government Buildings in Dublin on Monday evening.
Tweeting afterwards, Mr Varadkar said it was a "good meeting".
Mr Cook is travelling to Cork, to open an extension to an Apple facility there.
The meeting comes just over a month after the tech giant pulled out of plans to build a new data centre in Athenry, Co Galway.
Objectors to the proposed €850m facility had decided to take their case to the Supreme Court in December.
It followed a High Court judgement in November that seemed to pave the way for works to begin.
Apple had planed to build the state-of-the-art data centre on a 500 acre Coillte-owned site just outside Athenry.
But a number of local residents raised concerns about the potential environmental impact of the project - and accused An Bord Pleanála of not carrying out a proper assessment.
The Commercial Court also ruled against the objectors in October.
In a statement at the time, Apple said: "We've been operating in Ireland since 1980 and we're proud of the many contributions we make to the economy and job creation.
"In the last two years we've spent over €550m with local companies and, all told, our investment and innovation supports more than 25,000 jobs up and down the country.
"We're deeply committed to our employees and customers in Ireland and are expanding our operations in Cork, with a new facility for our talented team there.
"Several years ago we applied to build a data centre at Athenry.
"Despite our best efforts, delays in the approval process have forced us to make other plans and we will not be able to move forward with the data centre.
"While disappointing, this setback will not dampen our enthusiasm for future projects in Ireland as our business continues to grow."