Fianna Fáil's Jim O'Callaghan is reported to be under pressure from party colleagues to challenge Micheál Martin's leadership.
The Sunday Times has reported that he has been approached by TDs unhappy with the presidential-style approach used in the general election in which they lost eight seats.
However, there does not seems to be enough support to mount such a challenge.
The Dublin Bay South TD is also said to have been cold on the move.
Nonetheless, INM's Hugh O'Connell said a challenge to the leadership of Fianna Fáil is looking likely.
Mr O'Connell said: "The (reasons for the challenge) are the unhappiness with Micheál Martin and his approach to leadership of Fianna Fáil and his approach to the election campaign and there are people here hitting out at the presidential-style election campaign revolving around Micheál Martin, certainly that is the grounds on which Fianna Fáil ran the election.
"Obviously it didn't work, so there are questions around Micheál Martin's future now in Fianna Fáil more so than at any point now in the last 10 years."