Luke Ming Flanagan is poised to take the first seat in the Midlands Northwest constituency.
Results from the second count are due imminently, and with just over 124 thousand first preference votes, Deputy Flanagan is expected to take enough transfers to be elected to the European Parliament.
Sinn Fein's Matt Carthy will take the next seat, unless Mairead McGuinness takes more transfers.
Pat the Cope Gallagher said he's definitely still in contention for the fourth seat, and said transfers will be crucial for him.
"I can describe it as being more hopeful than confident - but now, having received the first count, I'm happy there's a gap in excess of 4,000 between myself and my running mate Thomas Byrne, and about 10,000 between myself and Marian Harkin," he said.
"The distribution of votes now in the second count will be very significant."