The peace campaigner and former UN assistant general secretary, Mr Denis Halliday, has expressed a tentative willingness to contest a presidential election in the autumn against Mrs McAleese.
Dublin-born Mr Halliday (63), who spends most of his time in New York, said he was willing to allow his name go forward if no other candidate emerged to campaign on social issues and against the war in Iraq.
"I would be happy to bring these issues up, to put them on the table for discussion with the other candidates, for the Irish people," he said. "If I really felt that there was nobody else who could do these things, which I find hard to believe, then of course I would be tempted to take up the challenge and play a part."
While President McAleese is expected to declare in the coming weeks that she will seek a second seven-year term, the only rival candidate to have emerged so far is the former MEP, Ms Dana Rosemary Scallan. Labour is still considering whether to contest the election.
Mr Halliday would need the support of 20 TDs and senators or four county or city councils to be nominated.
The independent Dublin TD, Mr Finian McGrath, who made the initial approach to Mr Halliday, said 13 TDs had indicated they would back him. Mr McGrath wants the independent TDs, the Greens and Sinn Féin to unite behind Mr Halliday as an independent candidate.
But Mr Halliday, a Quaker committed to non-violence, said Sinn Féin's links to the IRA would have to be the subject of "important discussions" assuming that party was interested in backing him.
Mr Halliday, who grew up in Terenure, left Ireland in 1962 and in 1964 joined the UN, where he rose to the rank of assistant secretary general. He retains his Irish passport.
He resigned as UN Humanitarian Co-ordinator to Iraq in 1998 in protest at UN sanctions against Iraq. He campaigned in many countries against the US-led invasion of Iraq last year.
While "slightly shocked" to have been approached by Mr McGrath, he said he would have an obligation to respond if no alternative candidate emerged.
Mr Halliday has a home near Clifden, Co Galway, and he spends about 10 weeks of the year in Ireland. He lectures for part of the year in Trinity College.
