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 talks this week.
Both parties are expected to outline how a minority Government would work - if they were to win the support of independents.
The Independent Alliance's Shane Ross - says while they've joked about gaining ministerial office - it's never been seriously discussed:
Meanwhile a former Fianna Fáil cabinet member says the party needs to reconnect with voters.
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: