The Independent Alliance has discounted claims it's been offered cabinet positions in return for supporting a minority Government.
Fianna Fáil and Fine Gael are set to lay out their proposals in historic talks this week.
Both parties are expected to outline how a minority Government would work - if they win the support of independents.
The Independent Alliance's Shane Ross - says while they have joked about gaining ministerial office - it's never been seriously discussed:
“We've negotiated with Fianna Fáil and Fine Gael for months, in open and in closed sessions, and they have never mentioned, and nobody has ever mentioned to me once, about a cabinet post.”
Meanwhile a former Fianna Fáil cabinet member says the party needs to reconnect with voters.
Speaking to Shane Coleman on the Sunday Show Noel Dempsey says rural Ireland believes the country's two biggest parties are not reflecting their interests.
He says his former colleagues need to go back to old tactics and engage people:
“I heard somebody yesterday from Sinn Féin talking about being out canvassing and everything else. That’s what Fianna Fáil started at, they went into every nook and cranny of every town.
“But over the period I was in government, and a period longer than that, Fianna Fáil seem to have withdrawn out of certain areas, ‘oh, we’ll leave that’ and go for the easier vote. So they have to reconnect.”