Three senior TDs have indicated they will put their names forward for leadership of the Labour Party.
A fourth, Brendan Howlin, said he would give the matter his "strongest consideration" over the weekend.
Eamon Gilmore, Joan Burton and Tommy Broughan have all expressed interest in the position but have so far declined to declare their candidacies until after further discussions with colleagues.
Liz McManus, who is the current acting party leader until a successor to Mr Rabbitte is elected, has also expressed an interest in the post.
Speaking on RTÉ radio yesterday, both Ms Burton and Mr Gilmore said they were considering the possibility of running for post but wished to consult with colleagues prior to declaring their candidacies.
Mr Broughan said he did not think anybody who had served in the Dáil would turn down the chance.