For years, Cardinal Carlo Martini has been the man liberal-minded Catholics have wanted to see on the papal throne.
But the lengthy pontificate of John Paul II led the cardinal's supporters to believe that his moment had passed. He is now 78, living in retirement, and not in good health.
However, he is still revered by the liberal wing of the Church, and in the days before the conclave, people have been talking about a symbolic candidacy.
Cardinal Martini: says Church must face up to problems of modern life
It is thought his name would attract a significant number of votes, particularly from those opposed to Cardinal Ratzinger.
Once that challenge was seen off - so the theory goes - the way would be open for Cardinal Martini's votes to be passed to a younger and healthier candidate.
Before his retirement, Cardinal Martini was Archbishop of Milan, the largest archdiocese in Europe.
He remains a respected biblical scholar who has written more than 40 books, and is reputed to speak 11 languages - an asset for any pope.
He has been described as the best-equipped intellectually and spiritually for the job. He has travelled widely and is regarded as a good communicator.
If elected, he would be the first Jesuit to become pope.
But while Cardinal Martini has been a favourite of the reformers, his views do not find favour among traditionalists.
For example, he has spoken of encouraging women to take a more active role in the Church by allowing them to become deacons.
On contraception, he once said: "I believe the Church's teaching has not been expressed so well... I am confident we will find some formula to state things better, so that the problem is better understood and more adapted to reality."
Less controversially, he has highlighted the plight of the poor and the elderly, and has expressed concern for the problems faced by immigrants in Italy.
He has also spoken out against racism, and has urged people to show Christian understanding for minorities and the marginalised sections of society.
But the key question is whether Cardinal Martini - or any other liberal for that matter - can win the votes of two-thirds of a predominantly conservative electoral body.
One Vatican expert, Father Thomas Reese, puts it this way: "Martini has got three strikes against him. The first is that he is a Jesuit, and we have never had a Jesuit pope, so I think that is a handicap.
"Secondly, just appearing to be a liberal counterpoint to John Paul - whether it's true or not - is not regarded as a good thing by the other cardinals. And third, he's gotten too much press coverage."
Cardinal Martini has certainly had a high profile, and has not been afraid to suggest that it is time for changes in the way the Church is run.
In a radio broadcast, he once talked about his desire to see a less centralised Church. This was seen as an implied criticism of the style of John Paul II, who said pointedly that some senior figures in the Church were giving too many interviews.
Cardinal Martini wants greater democracy in the running of the Church, a key demand of the reformist wing.
His ideas have provoked some sharp responses, an indication of the tension within the Church between progressives like Cardinal Martini, who are prepared to discuss a range of contentious issues, and conservatives who are trying to prevent change.
Cardinal Martini says the Church must face up to the problems of modern life, including such issues as sexuality, divorce, the celibacy of the priesthood, and the role of women in the Church.
He says the Church has to rekindle the "burning fire in the heart".
If his critics are correct, and he is just too liberal to be elected pope, he does have enough influence to be a grande elletore - a kingmaker whose views could sway the conclave.