But the leader of the Catholic Church in Ireland has asked Pope Benedict to appoint an "archbishop in waiting" to succeed him as Primate of All-Ireland if his health fails, according to church sources.
If the sources are correct, Cardinal Brady's decision to request the Vatican appoint a coadjutor archbishop of Armagh will mean that Rome will identify the cleric it wants to lead the church after his retirement on reaching 75.
Since revelations broke in March about his swearing to secrecy on oath in 1975 of two children abused by Smyth, Dr Brady has signalled his determination to carry on as "a wounded healer". Further doubts about his future arose in April when he took ill during Mass and was ordered by doctors to suspend public duties .
But the Irish Independent has learned that Dr Brady last week flew to France as leader of the annual Armagh diocesan pilgrimage to Lourdes. Church sources said it was expected Dr Brady will announce his decision to stay on in his dual role as Archbishop of Armagh and head of the Irish Bishops' Conference at the Marian shrine.
Previously, Dr Brady said he would make his decision known on Pentecost Sunday (May 23).
Unlike an auxiliary, or assistant bishop, a coadjutor archbishop has the automatic right of taking over a diocese in the event of death or incapacity of the current holder of the office.
Meanwhile, a parish priest has strongly criticised the Archbishop of Dublin, Diarmuid Martin, accusing him of "unfocused rants" in his recent comments on the child sex abuse crisis.
Fr Dick Lyng, the parish priest of St Augustine's in Galway city, said that while Dr Martin's comments in his address to the Knights of St Columbanus had been delivered to "predictable media acclaim", closer scrutiny of the text tended to dissipate one's enthusiasm.
Scandals
In last Monday's speech Dr Martin claimed that strong forces in the church wanted the truth about clerical sex abuse scandals to remain hidden.
But in his parish newsletter to massgoers yesterday, Fr Lynch asked: "Where did Archbishop Martin find this unwillingness, this resistance?
"Is it within his own diocese, among his fellow bishops, or within the Vatican itself? Bill Murphy (Bishop) of Kerry has more or less stood up and said and asked: 'Is it I, Lord?' Until this is clarified, the shadow of suspicion falls everywhere.
"This is, I fear, now characteristic of the archbishop's style: throw the grenade into the crowded room and then ask the intended targets to pull the pin themselves."
SIC: II