Adams refuses to comment on McGuinness running for President rumours
The next president must embody a broad democratic republican spirit, Sinn Fein leader Gerry Adams said.
As the party prepares to decide whether to field its own candidate, Mr Adams praised Mary McAleese, claiming the office was respected across the island.
But he would not be drawn on speculation that Northern Ireland's Deputy First Minister Martin McGuiness could be put forward to contest the race.
"We need a president who will embody the broad democratic republican spirit," Mr Adams said.
"We need someone who will not just feed us poetry, but who will actually in a very, very positive way face into the future because he or she trusts the people of Ireland, because he or she cherishes the people of Ireland, because he or she wants to see a real republic across the island."
The Ard Chomhairle of the party is expected to meet this weekend where Mr Adams is to recommend fielding a candidate.
Former Northern Ireland agriculture minister Michelle Gildernew has, along with Mr McGuinness, been touted as a potential contender, but Mr Adams said there had been no formal decision on who might stand.
The party leader said if they decide to support a candidate, he or she will not run specifically as a Sinn Fein contender.
Mr Adams and Mary Lou McDonald have both ruled themselves out of the race.
Independents Mary Davis and Sean Gallagher officially became candidates yesterday after each secured the support of at least four councils.
They are on course to fight it out with frontrunner Labour's Michael D Higgins and Fine Gael's Gay Mitchell.
Speculation has mounted that Independent Senator David Norris could reverse his decision to pull out of the campaign amid growing public support.
Fianna Fail leader Micheal Martin said the party would decide its approach to the presidential nomination process collectively.
Meanwhile Sinn Fein said it believes more than 3 billion euro should be raised in December's budget, but ruled out going closer to 4 billion euro.
Finance spokesman Pearse Doherty said the party will put forward its pre-budget plan well in advance of December's budget.