Two members of Fianna Fáil have expressed an interest in putting their names forward for the position of Ceann Comhairle in the next Dáil.
John Deasy, a Fine Gael deputy for Waterford, has also said he is interested in the role
The post will be filled by secret ballot when the Dáil returns next week.
It will be the first time the post in filled in such a way after measures were passed by the last Dáil in January.
Candidates must be nominated by seven other TDs before going forward for the vote.
Sean Barrett, the Ceann Comhairle in the last Dáil, said in February he would not be seeking re-election to the post.
Nominations of candidates for the role will have to be received by the Clerk of the Dáil not later than 6pm on 9 March - the day before the new Dáil meets.
Nomination forms will have to have the supporting signatures of at least seven other TDs and TDs can only nominate one candidate.
Should only one candidate be nominated, then there will be no secret ballot for the election of Ceann Comhairle.
TDs will vote in the division lobbies in the Dáil chamber and they will be allowed to vote for more than one candidate in order of preference.
In the same way as the general election is conducted, the votes will be counted under a Proportional Representation Single Transferable Vote system.