Mary Lou McDonald has praised her 'constructive' and 'useful' talks with Green Party Leader Eamon Ryan.
The Sinn Fein President has begun meeting with different parties in order to try form a Government of the left - without Fianna Fail or Fine Gael.
Speaking after their talks this morning, she told how they plan to meet again in the coming days.
She said: "I have made it clear since before the election - and after - that I will speak to all parties in the interests of forming a government; starting with those with a mandate for change.
"The Green Party, having increased its mandate significantly, is undoubtedly one of those parties.
"I met this morning with Eamon Ryan TD, leader of the Green Party, and it was a very useful and constructive meeting.
"We have agreed to begin exchanging ideas, and we will talk and meet again over the coming days."
Ms McDonald will also meet with People Before Profit's Gerry Carroll and Richard Boyd Barrett later today.
It comes just hours after Mr Boyd Barrett said Sinn Fein-led minority Government may not last long but it could still achieve progress and is "definitely worth exploring."
He told RTE's Morning Ireland: "It wouldn't be sustainable for very long but I still think it's worth exploring if we could do something to urgently address the housing crisis, some of the problems in the health service with the desperate waiting lists, some of the issues around climate change and the cost of living.
"I think anything that could give expression and delivery to the sentiment that people expressed at the ballot box during the election would be worth exploring and I am absolutely keen to do it and People Before Profit are absolutely keen to try to do that."
