Diaspora Minister Joe McHugh says the numbers could be huge
The number of people outside the State with a vote in Irish presidential elections could be as high as 3.6 million.
That is according to the junior minister responsible for drawing up the plans around the new scheme, which was announced on Sunday.
The Government is to publish a detailed Options Paper later this month to set out the options available.
This paper will also be one of the topics for discussion at the Global Irish Civic Forum, which will take place in Dublin in May.
The initiative, confirmed by Taoiseach Enda Kenny in Philadelphia, could potentially mean more voters outside the State than there are within it.
Diaspora Minister Joe McHugh says the number of voters could be huge.
"You're talking about - you're including outside the State - so for Northern Ireland 1.8 million, you're talking about another 1.8 million potential citizens internationally.
"So that's 3.6 - so you're talking big numbers here."
The announcement has been welcomed by a number of groups who have been campaigning for the right to vote for Irish citizens abroad.
The group, Votes for Irish Citizens Abroad (VICA), says extending the right is hugely important for people who had no choice but to leave Ireland for work.
Dean Duke, executive member of VICA says it is about time it happened.
"Most other democratic countries around the world give their citizens a say, regardless of where they're living.
"And I think that a lot of people have left Ireland - particularly in the last decade - who might want to come back some day and certainly still feel that connection to Ireland and want to have their say in shaping the country.
"So we think that extending the vote for the presidential election is a good start in that regard".
It has also been welcomed by Sinn Féin President Gerry Adams, who said the Government needs to "quickly clarify what this means in practice and when the referendum will be held."
While SDLP leader Colum Eastwood said it was "an important step in recognising the immense contribution that Irish citizens and communities across the world make to our island."
And Green Party spokesperson for political reform, Oliver Moran, said: "This is good news. It underlines the importance we attach to our Diaspora and citizens in Northern Ireland.
It places the president as the first among equals in the entire Irish nation, no matter where we live."