Dana Rosemary Scallon has announced her intention to seek a nomination for the Presidential election.
Speaking in Dublin she said she was asking the members of the Oireachtas to run as an independent candidate.
She would not divulge who was backing her but said she had some backers.
Speaking on RTÉ’s Six One News, the former MEP said it would be very, very important to get the support of Fianna Fáil TDs and Senators in order for her to secure a nomination for the Presidency.
She said she has the support of more than one independent Oireachtas member at this stage, but did not reveal how many supporters she had.
She said she has until 28 September to get the support and that while it was always difficult for an independent, the Oireachtas should open up the process for the Presidential election.
Ms Scallon has also said that there was a widespread desire for a more open process, adding that the day was gone when the keys of the Áras belonged to the political establishment.
Separately, Senator Labhrás Ó Murchú described a meeting today with Fianna Fáil party leader Micheál Martin as "constructive and amicable".
However, he said he is pressing ahead with his attempt to get the backing of individual Fianna Fáil parliamentarians to run as an independent candidate in the presidential election.
He said both men agreed not to discuss the content of the conversation ahead of tomorrow's Fianna Fáil parliamentary party meeting.
Senator Ó Murchú said there were likely to be further discussions between the pair before the meeting.
Earlier, Senator Ó Murchú said he has the required support of 20 Oireachtas members to be nominated.
Speaking on RTÉ's Today with Pat Kenny, Mr Ó Murchú said he would not take a salary if elected President because he would be honoured to serve in the Áras.
He said he had made up his mind to do this before Martin McGuinness' announcement to only take the industrial wage.
Mr Martin was also due to meet his deputy leader Éamon Ó Cuív in Dublin today.
Last week it was reported that Mr Ó Cuív threatened to resign over the issue.
Speaking on the Adhmhaidin programme on RTÉ Raidió na Gaeltachta this morning, Mr Ó Cuív said the only issue the party had to decide as regards the Presidential election was the question of supporting an independent candidate or candidates.
There was no question of running a Fianna Fáíl candidate at this stage, he said, but the party was in the process of conducting a healthy internal debate on the issue of independent candidates.
Mr Ó Cuív also rubbished suggestions that he was directly challenging the party leader.
McGuinness stands down from Stormont
Sinn Féin's Martin McGuinness has stood down as Northern Ireland Deputy First Minister in order to contest the Irish Presidency.
Mr McGuinness was officially ratified by the Sinn Féin Ard Comhairle yesterday after securing the support of four Independent TDs.
Stormont Education Minister John O'Dowd will fulfil Mr McGuinness' responsibilities while he contests the election.
Speaking to reporters this morning, Mr McGuinness said his past should not prevent him from being elected as President.
After being endorsed by the party's leadership, he said the Northern Ireland peace process would be strengthened by his involvement in the election.
Commenting today on Mr McGuinness' entry into the race, the Taoiseach said it does not put pressure on Fine Gael and he believes it brings the real qualities needed for the role into focus.
He said Fine Gael had the best candidate in Gay Mitchell.
Enda Kenny said the next president will have a fundamentally important role in building bridges both to older countries of Europe and beyond.
Asked specifically about Mr McGuinness, Mr Kenny said he would not comment on any other candidate. He said there is a process there for nominations.
Elsewhere, Mr Mitchell said Ireland is at an important crossroads in its history and he believed he had the experience and the energy to bring the country to "a happier place".
Speaking on Midwest Radio, he said he felt people had become far too hard, aggressive and judgemental in recent years and there was a need for a gentler society.
He said one of the issues that he hopes to devote himself to as president was to reduce the number of deaths by suicide, which has become a matter of great concern in recent years.
Referring to the upcoming 100th anniversary of the 1916 Rising, he said he would like to see the Dáil conferring powers on the president to organise events in 2016 to ensure that they will be of a truly inclusive nature.
He said he wanted to see a united Ireland but it was clear that a 30-year attempt to bomb Northern Ireland into the Republic did not succeed.