While speculation has focused on Parramatta's bishop, the Dominican friar Anthony Fisher, as a front-runner, senior church figures caution against jumping to conclusions.

When pressed to name likely candidates, the general secretary of the Australian Catholic Bishops Conference, Father Brian Lucas, replied: "I have a saying when it comes to the appointments of bishops. 'Those who talk, don't know; those who know, don't talk.' "

The few who are talking, privately, also suggest the Archbishop of Brisbane, Mark Coleridge, and the bishop of Newcastle and Maitland, Bill Wright, as contenders.

A local selection process will be led by Australia's Apostolic Nuncio, Archbishop Paul Gallagher, to find the best candidates. Archbishop Gallagher notes that Cardinal Pell is still Sydney's Archbishop and the position has not yet been declared vacant, but if the Pope makes that move – likely in the coming days or weeks – the Nuncio will start consulting senior church figures.

"You make the initial consultation with the bishops," Archbishop Gallagher explained. He then widens his discussions to "consulters" – priests who bishops have chosen to advise him.

"A number of them must also be heard. And when we determine a shortlist of possible candidates, we go deeper into the thing. One would assume the three candidates would already be bishops, but it's not necessarily the case. It's probably the case."

Who and how many among the laity would be consulted?

"It's very much left to my discretion," Archbishop Gallagher said. But the opinion of "qualified" non-clergy would be sought on the suitability of a particular candidate.

"For all these big jobs, the number of people who could be qualified [to be Archbishop] could be quite limited."

Age was also a consideration. "One is not going to appoint someone who is himself nearing retirement age." But experience mattered, he said, so it might not be a bishop ordained in only the last couple of years.

The Nuncio producers a "terna" – a dossier containing the three names – which is submitted to Congregation for Bishops in Rome, a department of the Holy See that makes recommendations to Pope Francis, who is expected to take a close interest in such a senior appointment.

Bishop Anthony, as Anthony Fisher is called on the Parramatta diocese website, is overseas on annual leave and was not available for comment on Tuesday. Born in 1960, he was only 49 – and the youngest bishop in Australia – when appointed to lead Parramatta in January 2010. However, Pope John Paul II had already named him as Auxiliary Bishop of Sydney in 2003.

He was baptised at St Therese Church, Lakemba, and attended that parish school before moving to St Michael's at Lane Cove, Holy Cross College at Ryde and St Ignatius' College, Riverview. He studied history and law at the University of Sydney and practised law in a city firm, and was involved in the "pro-life" movement.

In 1985, he entered the Order of Preachers, or Dominicans. He was ordained a priest in 1991, completed a doctorate in bioethics at Oxford in 1995, lectured at the Australian Catholic University, became a foundation director of the John Paul II Institute for Marriage and Family in Melbourne and adjunct professor at the University of Notre Dame and deputy-chancellor of the Catholic Institute of Sydney.

When named as Bishop of Parramatta, he said: "Priests are the backbone of our parish life ... Naturally, promoting priestly and religious vocations will be a major priority for me."

The 61-year-old Bill Wright – or Bishop Bill, as he prefers to be called – said soon after Cardinal Pell appointed him to the Newcastle-Maitland role in 2011: "In 33 years of being a priest I've only applied for one position; the rest found me. I've come to believe there's a certain 'providence that shapes our ends' – and, so far, things have turned out all right."

A Sydney University arts graduate with honours – largely in history – he also said: "I would like to see much more evidence of a church of ideas, so that at the heart of things, there are some very strong Christian religious ideas, instead of rote practices or 'emotional devotionals'.

"We believe that human reason can attain to truth, so I would like to see in Catholicism a church that really valued the intelligence and rationality of its people, that engaged with questions and sensible answers. Intelligent participation in public affairs, and life, is hard work. You can't just say, 'There it is, take it or leave it. If you don't believe that, you're not a good Catholic."'

Brisbane Archbishop Mark Coleridge, 65, has strong credentials as a bishop and through his work with the Vatican. A former master of the Catholic Theological College in Melbourne, he worked in the Vatican Secretariat of State from 1997 and was ordained Auxiliary Bishop for Melbourne four years later. In 2004, he was appointed as a member of the Pontifical Council for Culture and chair of the Roman Missal Editorial Committee of the International Committee for English in the Liturgy.

He became Archbishop of the Canberra and Goulburn in 2006, joined the Pontifical Council for Social Communications in 2011, and was appointed as Brisbane's Archbishop in April 2012.

Age may is likely to count against 72-year-old Denis Hart, Archbishop of Melbourne since 2001. The church is also likely to want a clean break from the church's past handling of child abuse complaints against clergy. At a parliamentary inquiry last year, while acknowledging a history of cover-ups, he defiantly denied police claims of a lack of co-operation since the church's 1996 Melbourne Response. He also said the church no longer dissuaded victims from going to police, and insisted that information on abuse gained through the confessional must remain secret.

Father Lucas warns: "Most people who speculate about successors in this area tend to get it wrong, the way they also speculated about who the next Pope was going to be. Absolutely not a single journalist in the world got Pope Francis right."

The Nuncio, Archbishop Gallagher, says of the local shortlist process: "We're talking months rather than weeks, although it is a priority appointment, so to some extent I expect we will try to fast-track it a bit."

Whoever prevails as the next Archbishop of Sydney, the biography of Mark Coleridge on his diocese website notes that he has been moved to reflect: “Jesus often surprises, but he never disappoints.”