Independent TD Shane Ross says that his group will come to a "speedy" decision once Fine Gael and Fianna Fáil put their final proposals to them.
“We will come to a speedy decision once we see the colour of their money,” said the Dublin Rathdown TD on the Pat Kenny show on Newstalk.
Mr Ross said he doesn’t think that a deal will be reached between Fine Gael and Fianna Fáil before the vote for Taoiseach this Thursday.
“It will take beyond that, but at long last they are talking and good sense has prevailed.”
Roscommon-Galway Independent TD Michael Fitzmaurice also welcomed the Fianna Fáil and Fine Gael discussions taking place on Monday.
“At least they’re talking now,” he said, adding that he expected an agreement for at least three budgets, but emphasised that neither side had said that.
“It is up to the Independents to decide who will lead this government. We have done everything as fast as we can.
“The main parties can now slow down or speed up.”
Mr Fitzmaurice expressed disappointment that a coalition had not been agreed. “I thought that in the interest of the country a coalition would have been a good thing.”
“At least they’re talking now. There are a lot of others who are hurlers on the ditch. They ran for the hills when they were elected and did nothing to make an honest attempt to form a government.
When asked on RTE's Morning Ireland if he expected a Cabinet seat, he replied "I drive up to Leinster House in a van. I don't give a damn if I have a Merc or a Mini. Everyone who is elected aspires to be a Minister, but you have to be realistic."
Meanwhile, Kerry Independent TD Michael Healy Rae has refused to rule out the possibility of a Fianna Fáil-led minority government.
Speaking on RTÉ’s Morning Ireland, he acknowledged such an option was unlikely, but added “I never say never”.
He said: “It’s all up in the air until it comes down to the ground.”
He welcomed the talks taking place between Fine Gael and Fianna Fáil. “I would hope that the road ahead will become clear. We have to know the practicalities of how it will work day by day.
“We don’t want the whole thing to collapse at the first hurdle. We want it to last a considerable length of time. We know it won’t last five years,” he said.
“I just hope a sound foundation can be laid.”
When asked what specific issue he wanted included in any Programme for Government, he said wanted the creation of a rural affairs ministry “to be in charge of rural-proofing all government policies.”
Waterford Independent TD John Halligan said the lack of a 24-hour cardiac unit at Ardkeen Hospital in Waterford will be his deciding factor in who to support in the government formation talks.
“Waterford has suffered disproportionally - it is the only hospital in the country without 24 hour cardiac care. If you have a heart attack after 4pm on Friday you will have to go to either Dublin or Cork.
“I hope it won’t come down to the hospital. I will make a decision based on what is happening with Fianna Fáil and Fine Gael,” he told Newstalk radio.
Fianna Fáil and Fine Gael negotiating teams are set to commence formal talks later today with a view to agreeing the shape of a minority government that could run for 2½ years.
The initiative was agreed between outgoing Minister for Health Leo Varadkar and Fianna Fáil TD for Dublin Bay South Jim O'Callaghan, at the latter's home on Saturday morning.
Following bitter exchanges between the parties last week following Fianna Fáil’s rejection of Fine Gael’s partnership plan, Fianna Fáil and Fine Gael were involved in back-channel communications ahead of the weekend.
According to those close to the process, there is now a clear understanding the focus is on a minority government, probably led by Enda Kenny.