Mr Kelly said Fine Gael supporters feel “sidelined” after Sinn Féin decided it will field a candidate and amid a growing number of potential Independent candidates.
Dragons’ Den star and businessman Gavin Duffy also confirmed he is “considering seeking a nomination” for the presidency.
It comes as Fianna Fáil confirmed its councillors will now be able to support a candidate, throwing open options for those in need of councils to run.
A candidate for the presidency needs to be over the age of 35 and requires the support of 20 Oireachtas members or four councils.
Campaigns for a race are now heating up, with several figures indicating a desire to challenge Michael D Higgins’ ambitions for a second seven-year term.
Mr Kelly told the Irish Examiner in January that he would like to run. The Ireland South MEP said that Taoiseach Leo Varadkar and Fine Gael should consider rescinding support for President Higgins.
Fine Gael’s national executive is due to meet this week and is expected to confirm support for the incumbent.
Mr Kelly said: “Fine Gael supporters have approached me who aren’t pleased we are not running a candidate, especially with Sinn Féin running one. They feel sidelined.”
It is understood that, at Fine Gael’s parliamentary meeting in Leinster House last week, Louth TD Peter Fitzpatrick suggested Mr Kelly or fellow MEP Mairead McGuinness would make good candidates.
Mr Kelly said: “Supporters are saying we are off the pitch.
Meanwhile, It is understood that Mr Duffy is targeting nine councils for votes and will make an announcement next week. He said: “I haven’t ruled it in or out. I am considering seeking a nomination.”
It is understood Seán Gallagher, who came second in the presidential election in 2011, is working with Mr Duffy. Mr Gallagher wrote to councils last week asking them to facilitate candidates.
Sinn Féin will not make a decision about who to run for two to three weeks at least. A number of cúige, or regional committees, will recommend a name or names to the leadership.
Sinn Féin TD David Cullinane, who is overseeing the process, confirmed that the option of allowing Sinn Féin councillors back a separate or non-party candidate is also being considered.
Fianna Fáil sources yesterday confirmed its councillors will not be subject to a whip, despite a decision by party Oireachtas members and leader Micheál Martin to back President Higgins for a second term.
A story in yesterday’s Irish Examiner said a nomination is possible if 20 councils support an individual, rather than the correct figure of four.