Former Minister Mr Michael D Higgins has said the Labour Party will not decide until next month if it will contest the presidential election in November.
The President, Mrs McAleese, who was backed by Fianna Fáil and the Progressive Democrats in 1997, is expected to announce her decision to seek another seven-year term early next month.
However, Mr Higgins said there was little doubt that she would seek a second term.
"Her activities recently would suggest that she is interested in going again.
"It is a bit intensive to be a swan-song," said the Galway West TD, who would be Labour's most likely candidate if it chose to fight the election.
Insisting that the decision has not yet been taken, Mr Higgins said his own circumstances "had changed since the spring" following operations in June to replace seriously arthritic knees.
Still on crutches following his operations, Mr Higgins said the knee replacements had been successful.
"I hope to return very vigorously in the autumn."
He said the presence of the osteo-arthritis in his knees was only discovered last December, but it progressed "very quickly" during the following months.
Though most Labour colleagues believe that Mrs McAleese could not be beaten in an election, Mr Higgins said this was not the issue.
Labour was keener on running a candidate last spring after the leader of Fine Gael, Mr Enda Kenny, made it clear that he would not be running a candidate. However, the cost and the prospect of a runaway victory by Mrs McAleese has dampened enthusiasm since.
Mr Higgins said however: "The issue is not whether she is beatable or not. The issue is the presidency, its independence from Government, its usefulness," he told The Irish Times yesterday.
Labour's national executive will discuss the possibility of contesting the presidential election when it meets in the middle of next month following a meeting of the party's parliamentary party.
"We had a brilliant local election campaign in Galway. We are the biggest party now. I was the director of elections. Now everybody has gone on holidays.
"I had a meeting with Pat Rabbitte a couple of weeks ago. We discussed the presidency, but no decisions were taken," said Mr Higgins.
A decision by the Labour Party not to run could mean that Mrs McAleese could be appointed for another term by the Oireachtas without a contest.
Independent TDs have made little apparent progress in their attempt to run former United Nations official Mr Denis Halliday for the position.
Meanwhile, former Independent Connaught-Ulster MEP Ms Dana Rosemary Scallon has not yet indicated if she will seek a nomination for the position.
She would require the support of four county councils, though this could be more difficult for her to achieve following Fine Gael's decision not to run a candidate.