Fianna Fáil MEP Billy Kelleher has stepped up his bid to become a presidential election candidate and has approached colleagues seeking their support.
The party's process to select a candidate is expected to be set out in the coming days.
The final decision will most likely be taken after a vote of the Fianna Fáil parliamentary party next month.
There were indications that an initial party meeting on the matter could be held next week but none has been scheduled to date.
There is thought to be strong support for Jim Gavin within the senior ranks of Fianna Fáil.
A number of TDs confirmed that they had received calls from prominent party figures canvassing for the former Dublin football manager.
Senior party figures suggested that if he got the endorsement of the leader, he would be selected by the parliamentary party.
Elsewhere, Sinn Féin is still considering its approach to the election amid a growing sense in the party that it should back Catherine Connolly.
It is understood that the party is still trying to make an assessment as to whether the Independent candidate can win the election.
Sinn Féin has been encouraged by Ms Connolly's views on a United Ireland.
Speaking in Belfast, she said that she would use her voice "in every way possible" to attempt to secure Irish unity should she succeed in her bid for Áras an Uachtaráin.
Ms Connolly also said that she wanted to see citizens of Northern Ireland being allowed to vote in future presidential elections.
She denied that she was using a visit to the west of the city to "court" Sinn Féin support.
Ms Connolly said political parties that have not yet decided on whether to run a candidate for the presidency are "disrespecting" the role and the Constitution.
"In relation to the parties that haven't made a decision, I would say on a general basis it's disrespectful to the Constitution and the role of the presidency that the parties haven't picked candidates yet for this very important role and that they are putting it off.
"On occasions it feels a bit like Lanigan's Ball, I stepped out and she stepped in again."
If Sinn Féin is to run its own candidate, and as leader Mary Lou McDonald appeared to dampen speculation about a run for the Áras, there is a view in the party that Pearse Doherty could be an effective option.
Separately, it is understood that former Labour junior minister Joe Costello has been asked to give advice to Ms Connolly's campaign team and they will meet shortly.
Mr Costello was campaign director for Michael D Higgins' successful presidential bid in 2011.
Councils to hold special meetings for Áras hopefuls
More councils have confirmed that they will hold special meetings from aspiring presidential candidates hoping to get on the ballot paper.
Tipperary County Council has confirmed that ten people have contacted the council seeking to get a nomination.
These include Gareth Sheridan and Nick Delehanty.
Potential candidates will be allowed to give a five-minute presentation of their manifestos at the special meeting. This will be followed by a ten-minute question and answer session.
Kerry County Council has also received requests from ten potential candidates. The candidates will be facilitated to present their case in person.
The council will later decide whether it will nominate anybody for the Presidential Election before deciding on a candidate.
Individuals need the backing of four local authorities to get on the ballot paper for the Presidential Election.
Dublin City Council and Kildare County Council have already pencilled in dates but these meetings will not be formally scheduled until the date for the election is set.
This will happen when the Minister for Housing James Browne makes the Presidential Election Order which sets out the polling day and the deadline for nominations.
Mr Browne is expected to sign the order next week in order to facilitate an election in late October.
The full list of individuals who contacted Tipperary County Council is: Dominick Plant, Gareth Sheridan, Cora Stack, Joseph Chikelue Obe, Nick Delahanty, Sarah Louise Mulligan, Cabdi Ní Chianáin (Charlotte Keenan), Paudie Dineen, Barry Wheely-Row and Lorna McCormack.
The full list for Kerry County Council is: Keith Mc Crory, Joseph Chikelue Obe, Domnick Plant, Barry Wheely-Row, Conor O'Brien, Nick Delehanty, Paudie O Dúinnin, Cora M Stack, Searlait Ní Chiannain and Gareth Sheridan.
Additional reporting Pat McGrath, PA
