President Mary Robinson's decision to leave the post, after accepting a senior United Nations appointment, has generated problems over the succession in Dublin.
While four candidates were openly jostling for the job, opinion soundings rated the still-undeclared Mr Hume, 60, Ulster's Social Democratic and Labour Party boss, as the clear favourite.
So far, the most serious contender to emerge has been Albert Reynolds, the former Prime Minister, who worked closely with Mr Hume in efforts to resolve the Northern Ireland conflict.
He is facing strong pressure to withdraw, however, if Mr Hume decides to give up the leadership of his party and membership of both the House of Commons and the European Parliament - as well as his key role in the revived peace process - to contest the presidency.
Two other possible candidates, Fine Gael opposition party rivals Mary Banotti and Avril Doyle, are likely to step aside voluntarily if Mr Hume indicates a firm interest in taking over from Mrs Robinson when she becomes the UN's Human Rights Commissioner next month. The position of another potential runner, Rosemary Brown, better-known as Dana, Ireland's first winner of the Eurovision Song Contest in 1970, has still to be clarified.
Dana, 44, an anti-abortion campaigner, and devout Roman Catholic now based in Birmingham, Alabama, where she presents a television show, was arriving in Dublin last night to step up her campaign for the presidency.
Pilgrims at Ireland's top marian shrine in Knock, Co Mayo, have already staged a support rally for Dana.
The reality is, however, that the entertainer will not be endorsed by the 20 members of the Irish Parliament necessary to secure her nomination to run for the presidency, which attracts a salary of pounds 100,000 a year.
Observers think that Mr Reynolds is currently the most likely next president, believing that his responsibilities to the peace talks will count out Mr Hume.
But the 65-year-old ex-taoiseach - at the centre of a marathon libel court tussle with the Sunday Times last year - could still be opposed from within the ranks of his own Fianna Fail party.
An election for the Irish presidency - if it is necessary - will be held on October 30.Reuse content