Brendan Howlin, Jan O'Sullivan and Sean Sherlock are still considering their positions ahead of the deadline for nominations
Alan Kelly has indicated he wants to see a contest for the Labour leadership.
So far he is the only TD to publicly put his name forward, as tomorrow's deadline for a decision approaches.
However, the Tipperary TD and former minister said he believes Labour members should have their say in the election of a new leader.
The Labour deputy leader refused to say whether or not he has a seconder to back him as a candidate for the leadership.
Brendan Howlin, who is seen as Kelly's main leadership rival, did not say if he would run - but added that the party was bigger than the leadership.
Alan Kelly believes that there should be a contest to replace Joan Burton, saying "I believe contest is healthy":
Brendan Ryan and Willie Penrose have ruled themselves out of a leadership bid, while Brendan Howlin, Jan O'Sullivan and Sean Sherlock are still considering their positions.
Deputy Howlin says their focus is on what is best for the party rather than trying to grab at the top job, suggesting "it's certainly not my ambition to have any particular job":