Green Party leader Eamon Ryan has said he is "nervous" and is revising downwards his forecasts for the party although he is holding out hope for strong transfers from other parties.
The party had previously hoped to win 15 seats.
"I think at this stage we would be more looking around the 10, 12, 13 mark," he said. "But you never know, in those marginal seats if we get transfers the way we historically do we will think maybe 15."
"I am nervous because we have had a great campaign and team. I've never seen a bigger effort, particularly on the ground. I think we are in with a chance of double figures and if we do that it will be a good day for us.
"In the local elections we only got five and a half per cent of the vote, if that exit poll is accurate and we are up at eight per cent, I will be very pleased with that.
"Hopefully it will translate in those last seats."
He said the last counts will "tell the tale today".
In Dublin Central, Neasa Hourigan has a "very good chance" of winning a seat, he said, as does Ossian Smyth in Dun Laoghaire.