The four Independent Ireland TDs will meet later this morning to decide if they will support barrister Maria Steen's campaign to get on the presidential ballot paper.
Ms Steen, who met the party last night to make her case, requires 20 signed nominations from either TDs or Senators.
The deadline for the close of nominations is tomorrow.
Aontú leader Peadar Tóibín said that 12 Oireachtas members have already signed Ms Steen's nomination papers and two more have indicated they will follow suit today, albeit that Mr Tóibín did not name them.
But if that proved to be the case, and Independent Ireland also backed her, Ms Steen would have 18 nominations - just two short.
Deputy Tóibín is engaging with other parliamentarians to see if they would back her but, once again, did not give their identities.
Initially, eight Oireachtas members signed up to back Ms Steen.
They are Mr Tóibín, Paul Lawless TD, Senator Sarah O'Reilly, Mattie McGrath TD, Carol Nolan TD, Senator Joe Conway, Senator Rónán Mullins and Senator Sharon Keogan.
Minister of State Michael Healy-Rae subsequently said he would back her as did deputy Gillian Toole.
Independent TD for Dublin Mid-West Paul Gogarty indicated he may add his nomination and there has been speculation about Danny Healy-Rae also.
Independent deputy Barry Heneghan said he would not nominate her, as did Senator Tom Clonan and Senator Gerard Craughwell.
The position of some Oireachtas members is unknown, like Senator Michael McDowell and Senator Victor Boyhan.
Over the weekend, there was speculation that two Fianna Fáil politicians were considering backing Ms Steen - even if it risked expulsion from the parliamentary party as a result.
