Delegates at the Fianna Fáil Ard Fheis are calling on the party to reject any coalition deal with Fine Gael.
They have also asked the party to oppose any coalition where they would be the smaller party.
Ann Murphy tabled the motion against Fine Gael, and she says the parties are not natural partners.
Ms Murphy said: "There's a certain element in the Fianna Fáil Parliamentary Party at the moment who are seriously thinking of going into government with Fine Gael after the election.
"I do not want to have it that my vote, when I give it for Fianna Fáil, will be going into Fine Gael, because we differ completely on many, many major aspects."