As parties across the political divide hold talks in a bid to form a government, Sinn Fein has its eyes firmly set on the left.
Mary Lou McDonald said her preference is to form a coalition that does not include Fianna Fail or Fine Gael.
The Sinn Fein president made it clear she will hold talks with the smaller left-wing parties including the Greens, Solidarity-People Before Profit, the Social Democrats, Labour and a number of Independents.
Before the outcome of the election was clear, the smaller parties all said they would be willing to talk to anyone, however Labour leader Brendan Howlin previously said that while he will talk to Sinn Fein, the Labour party has ruled out going into government with them.
Some of the parties will meet over the coming days to discuss the possibility of forming a Sinn Fein-led government and what their red lines will be before entering any talks.
Following the conclusion of the counts, Fianna Fail has the most seats after returning 38 TDs, followed by Sinn Fein on 37, and Fine Gael behind on 35.
The Greens now have 12 seats, the Social Democrats on six, Solidarity-People Before Profit on five and Labour has six, while Aontu kept its one seat.
The rest of the Dail is made up with 19 Independents.
Dun Laoghaire TD Richard Boyd Barrett said he will be meeting with other parties in the next few days.
But if you look at the numbers, much as we campaigned for and suggested that a left government was possible, I think probably we haven't got the numbersRichard Boyd Barrett
The Solidarity-People Before Profit TD, however, cast doubt over whether Sinn Fein has the numbers to make up an alternative coalition.
He told Newstalk: “There has been something of an earthquake in terms of Fianna Fail and Fine Gael now having considerably less than 50% popular support.
“It’s a poor result for the establishment, and we’re glad that many people have made that move.
“But if you look at the numbers, much as we campaigned for and suggested that a left government was possible, I think probably we haven’t got the numbers.
“I think there will be discussions among parties of the left over the next week about what can be done, but it would appear we don’t quite have the numbers.”
He added that the numbers in the Dail may not be there.
He added: “I would imagine there will be discussions between Fianna Fail and Fine Gael about the possibility of forming a government.
“Sinn Fein and Fianna Fail and possibly the Greens might have the numbers for a government.
“I think the priority for us is how do we keep the momentum to the left going, and look at how could the left build an alliance if we haven’t quite got the numbers for a left government this time around, it’s tantalisingly close.”
Meanwhile, Aontu leader Peadar Toibin, who resigned from Sinn Fein over his views on abortion, told RTE Radio One that he is speaking to a number of rural Independents in an attempt to form a group that could participate in the coalition talks.
He added: “What we are looking at doing is to see if we can build a common platform of objectives which would be core to any future government and then potentially negotiate to have those objectives included in a programme for government.”