It is believed there is some argument within the Fianna Fáil party as to whether it should put forward its own candidate for the Presidential election.
Party leader Míchéal Martin contacted broadcaster Gay Byrne at the weekend and told him that the party would give him its support if he decided to run as an independent candidate.
However, some members of the party are said to be angry Mícheál Martin did not consult them beforehand.
Former Fianna Fáil Minister Martin Manseragh said a lively discussion was now underway within the party, but that no decision had been made as to whether they would put forward their own candidate from within the party.
However, he said he would be in favour of backing Gay Byrne.
"He is a national institution…I think he would be a very worthy candidate," he said.