The Fine Gael and Fianna Fáil parliamentary parties are to meet separately today and it is expected they will discuss coalition options which are expected to lead to more detailed discussions with Independents and others.
The Independent Alliance which had six of its candidates elected has already reached out to a number of other Independents.
Independent Alliance member John Halligan said none of the main parties had contacted them but said that they are “willing to meet anyone who wants to meet us”.
“Something will have to happen and people will have to talk,” the Waterford TD said.
“We are going to attempt to get more of the Independents who have been elected to join with the Independent Alliance so we will be acting as one group,” he said.
Newly elected Independent TD Catherine Zappone said she will be taking the lead in making contact with parties and other groupings.
The outgoing senator who won a seat in Dublin South-West said has yet to receive a call from any of the major parties but will instead be writing to them.
“As an Independent I am very keen to participate,” she said.
“I would like to at least provide them with the offer. As an Independent senator I worked cross party to do a lot of my work,” she said.
It is understood the Green Party has spoken informally to five or six parties and groupings. However, these conversations have been extremely casual and did not involve any significant negotiations.
Likewise, the Social Democrats has had informal contact with some parties.
A senior Fine Gael TD is understood to have called party leader Eamon Ryan in the first overtures towards the party.
Tipperary Independent Mattie McGrath confirmed he had received contact from other Independents and parties.
While Dublin Central TD Maureen O’Sullivan said she had not had any contact with the larger parties but has been engaged in “casual talks” with other elected Independents about forming a technical group.
Michael Healy-Rae said both he and his brother Danny, who both won seats in Kerry, have been receiving calls. “There has been phonecalls going this way and that way but I am not going to say who from,” Mr Healy-Rae said.