Both Fine Gael leader Simon Harris and Fianna Fáil leader Micheál Martin have said Independent TD Michael Lowry is not a "kingmaker" in talks to form the next government.
Mr Harirs said the membership of the Regional Independent Group is a matter for them and not Fine Gael.
His comments follow confirmation from the gardaí that a file has been sent to the Office of the Director of Public Prosecutions following their investigation in the wake of the Moriarty Tribunal which investigated the awarding of the State's second mobile phone licence to businessman Denis O'Brien.
Mr Lowry was communications minister at the time and was found by the Tribunal to have imparted information to Mr O’Brien which helped him secure the licence.
Speaking at the at the BT Young Scientist and Technology Exhibition in Dublin, Mr Harris said his party had yet to sit down with the regional independents as a group, but said it is a matter for them who negotiates on their behalf.
Mr Harris said his party's negotiating team worked until midnight last night and was back working early this morning, adding that he hoped a government would be in place by 22 January, even if this was an ambitious goal.
Meanwhile the Fianna Fáil leader said his party will be negotiating with a group of Regional Independent TDs and it is up to that group who they want to appoint to lead those talks.
The Tánaiste acknowledged that he made calls in 2011 for Mr Lowry to resign as a TD following the findings of the Moriarty Tribunal.
"I did say that. But every general election since then, the people of Tipperary have taken the decision in terms of who represents them in Dáil Éireann," he said.
Mr Martin said Mr Lowry would not be a minister in that government, if those lead to a government being formed.
In such circumstances, a member of the Regional Independent Group would be a minister at some level, and they would be the "interlocutor" with the other parties in the government.
Mr Martin would not be drawn on whether he "trusted" Mr Lowry and said he had to be careful about what he said given that a file has been sent to the DPP following on from a long-running garda investigation into the findings of the Tribunal.
Asked if this development has changed his considerations around government formation talks, he said: "I have to be very careful what I say, given that this file has gone to the DPP.
"I have to be mindful of the independence of the DPP and also anything that would in any way undermine or impact on the progress of such an investigation and the subsequent potential court proceedings if that were to materialise."
Asked if he had any concerned now about negotiating with Mr Lowry, he said: "There are issues in the context of what has transpired now to be reflected on."
But he added: "I am not going to comment in any way that could potentially be used subsequently to impact or influence any case or due process."
Regarding Mr Lowry's role in negotiations, Sinn Féín Deputy David Cullinane said both Fianna Fáil and Fine Gael previously supported a Dáil motion to censure the Independent TD in 2011.
But, he said, "here we are with Lowry leading independents at the heart of government formation talks".
"The bottom line is I don't believe that these three groups will deal with the big and substantial issues that need to be dealt with," he said.
Mr Cullinane added Fianna Fáil and Fine Gael have no excuse for delaying forming a government as there is no difference between them regarding policy.
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Negotiations progressing
Talks to agree a new programme for government between Fianna Fáil and Fine Gael are continuing, with the parties expected to focus on childcare, disability, justice and health.
Discussions with Independent Ireland are also expected to take place.
Plans to allow members of Fianna Fáil and Fine Gael to vote on any agreed programme for government are being advanced by the two parties.
Under their rules, members must support the programme before the parties can enter government.
When a programme is agreed by negotiators, Fine Gael will hold five regional meetings at which attendees will be addressed by at least one member of the parties' negotiating team.
Each meeting will be followed by a vote, with only those with two years membership of the Fine Gael entitled to vote.
These meetings will be followed by a parliamentary party meeting where TDs, senators and MEPs will again vote on the programme.
Under the weighted voting system used by the party, the membership vote is worth 30%, councillor votes are worth 15% and the parliamentary party vote is worth 55%.
Fianna Fáil intends to hold a special national Ard Fheis to put any agreed programme to its members.
No information on a possible venue has yet been given.
Members of the party who attend the Ard Fheis will then get the opportunity to vote on the programme.
Independent TDs who support the programme may also hold meetings with their supporters to discuss its contents, but they are not bound by any formal rules in this regard.
There remains an ambition to conclude this process in time to have a government in place on 22 January.
However, several figures working on the new programme for government feel this is too optimistic a timescale and an extra week or more might be required.
The negotiators are set to work through the weekend and it is likely that discussions with the Regional Independent Group, and Michael and Danny Healy-Rae will also take place from tomorrow onwards.
In a statement this evening, Michael Healy-Rae said the Healy-Rae team had met with Mr Harris this afternoon in relation to forming a new government.
"The meeting was very positive and productive, we had an hour long discussion in relation to policy platforms and the Healy-Rae team supporting an incoming government," the statement said.
"We agreed that we would meet both party leaders together and their negotiating teams over the coming days," it added.
The Regional Independent Group has finalised a policy document, which they want reflected in the programme for government.
It contains constituency issues but also proposals around the affordability of homes, the quicker delivery of major infrastructure projects and ways to improve road safety.
Additional reporting Mary Regan, Mícheál Lehane, Joe Mag Raoillaigh
