Mr Kelly told Extra.ie that he would ‘probably’ decide today whether he wanted to put his name forward for the race. However, there is growing controversy over Senator Martin Conway, Mr Kelly’s potential replacement in Brussels.

Senator Conway, the first in line to replace Mr Kelly should the latter be elected President, resigned from the parliamentary party earlier this year after he was arrested for intoxication on Dublin’s O’Connell Street. It also emerged that he is at the center of the "inappropriate behavior" investigation within the party.

Mr Kelly could replace Mairead McGuinness as Fine Gael’s candidate after she dropped out of the race for health reasons. However, the party leadership is understood to now be weighing in behind former minister Heather Humphreys.

Senator Conway’s future looms over Mr Kelly’s Áras ambitions. Under EU parliamentary rules, there are no by-elections for the European Parliament. Instead, a party submits a list of potential replacements in the event that they die or resign from the office.

Senator Martin Conway.

Senator Martin Conway.

Mr Kelly’s list had John Mullins, the recently deceased businessman, as his first replacement, with Mr Conway second. Asked by Extra.ie if he had spoken to Mr Conway or asked him to step aside, or whether he was happy for the senator to become an MEP, Mr Kelly said: "Nothing to do with me or MEPs. It’s a matter for the party."

Sources in Fine Gael say Mr Conway, who is no longer a member of the parliamentary party, would not be approved to become an MEP if Mr Kelly won the Presidential election.

One source said: "It’s easily squared. Martin is second on the list. It will be bypassed.

 "The investigation [into Senator Conway’s behavior] has only started since he returned to Leinster House, so they’re going to make sure that the investigation won’t be over until November or December. So they’ll say they can’t pick someone who is subject to an internal investigation into the party."

The source said the party could move on to junior minister Jerry Buttimer, who is third on the list to step in as MEP, or Senator Eileen Lynch, the fourth choice.

Jerry Buttimer.

Jerry Buttimer.

"I assume Jerry would take it," the source said. "There are two things they’re investigating that are going back a long period of time, there’s no chance [the investigation will be resolved]."

The Fine Gael rulebook on replacing MEPs states: "The Executive Council shall determine the arrangements for the composition and ranking of the MEP replacement list in respect of the Fine Gael European Parliamentary representation."

Members of the party hierarchy have also moved swiftly to deny that Mr Conway – the first visually impaired member of the Oireachtas – would be the replacement, with one senior source claiming "whoever is saying this is being mischievous".

Former Fine Gael TD Heather Humphreys.

Former Fine Gael TD Heather Humphreys.

Others said Tánaiste and party leader Simon Harris would ensure that the issue did not come to dominate the Presidential election. However, experts on the rules of the European Parliament were more cautious, with one saying: "Once your name is attached to one of those documents, it is impossible to take them off."

A source supportive of Mr Conway said: "The hierarchy can spin all they want, but it is there in plain English that Mr Conway is the designated successor to Mr Kelly."

Mr Conway did not respond to a request for comment.

While the party hierarchy appears to be swinging behind Ms Humphreys, with some new TDs publicly backing her alongside Independent TDs who are supporting the Government, there are also some misgivings about her ability to win the race.

One well-placed source said: "She’s dreadful [with] the media and that’s the winning of the Presidential race… The one thing you’re guaranteed with Seán is a big vote – even if we don’t win, we get a good vote.

"Heather is unproven. She gets 10,000 votes in Monaghan, but she hadn’t gone for election in five years. Seán went last year and got 100,000 votes. I could be reading it wrong. Either way, we are goosed – Mairead was our only option."

Sources also pointed to Ms Humphreys’s stewardship of the care referendum, which the last government lost. She has experience as Minister for Rural and Community Development and Minister for Social Protection, but the source added: "My children could run Rural Affairs and Social Protection when no one is unemployed – it’s easy."

Dún Laoghaire TD Barry Ward is said to be a name that some are considering backing if Ms Humphreys ultimately decides not to put her name forward. Fine Gael did not respond to a request for comment.

* This article was originally published on Extra.ie.