Sean Kelly is set to become the first MEP elected in Ireland South on Monday.
An announcement for the first count is expected at around 1pm Monday after counters, who struggled with the 2ft-long ballot paper, are set to be sent home at around 11pm tonight.
Speaking at the count centre in Nemo Rangers GAA club, Mr Kelly was confident that the party is still in contention to win two seats in Ireland South despite exit polls suggesting that running mates Deirdre Clune and Andrew Doyle could be in trouble.
Mr Kelly, who looks primed to top the poll and to be elected on the first count, said transfers could still play a big role in determining who is elected in the coming days.
"I think we are still very much in contention for two seats, definitely if it is a five-seater but also if it is a four-seater," he said.
Although no formal tallies were conducted, Fianna Fáil's Billy Kelleher, Green party candidate Grace O'Sullivan and Sinn Féin's Liadh Ní Riada were performing strongly on first preferences.
Independents 4 Change candidate Mick Wallace, who will be in the hunt for one of five seats, said he is not nervous about the vote, despite suggestions that Fianna Fáil might be performing better than the exit polls indicated.
RTE's exit poll put Mr Wallace, who also attended the count, just 1% ahead of Malcolm Byrne.
"It's going to be very close," Mr Wallace said.
"I heard that Fianna Fáil are doing better than the exit poll showed and that would be problematic because Malcolm Byrne is a competitor for the fifth seat. If he does better, it is more difficult for me.
Mr Kelleher said transfers and eliminations would be a big factor as to whether Fianna Fáil can get their two candidates elected.
"Like any candidate you are always anxious. It will be a very long count, there are 23 candidates so there will be eliminations from very early on and many factors will come into it including geographical ones depending on which candidates are eliminated first," said Mr Kelleher.
Meanwhile, Green Senator Grace O'Sullivan said the party's performance was the result of hard work. She said the party's message is hitting home and that people can see through the "bluff" and "electioneering" of other parties.
"I am hoping that the surge that we are seeing around the country will bring home but it is early days," she said. "I'm hoping that I am lucky enough to be elected."
Liadh Ní Riada, who attended the count centre alongside party leader Mary-Lou McDonald, said she was not assuming anything or expecting to be a shoo-in.
"You are never fully confident and you are just hopeful and that's exactly the position I in am now. It's not over until all the counts are voted and that's when you can have some idea of where we are at," Ms Ní Riada said.
However, she said that overall it had been a disappointing election for the party, especially at local level where the Sinn Féin party suffered a significant loss of seats.