Roscommon-Galway TD Martin Daly believes Fianna Fáil and Fine Gael need eight more TDs to form a stable government.
They're only two short of an overall majority, with Fianna Fáil on 48 and Fine Gael on 38.
Both are ruling out a coalition with Sinn Fein, who are on 39 seats.
Potential coalition options for Fianna Fáil and Fine Gael include the Labour party and Social Democrats, both on 11 seats; Michael Fitzmaurice's Independent Ireland, on four; or a group of Independents.
Fianna Fáil will consider their coalition options at 12 noon today, at their first parliamentary party meeting since the election.
Deputy Daly, from Fianna Fáil, says there are several choices.