Scotland's Keith O'Brien recused himself last month after allegations dating back to the 1980s surfaced.
"My sexual conduct has fallen below the standards expected of me as a priest, archbishop and cardinal," he said Sunday, days after resigning his post and retiring.
A string of new scandals and allegations have emerged since Benedict became only the second pope in the Church's 2,000-year history to step down of his own free will.
The Vatican meetings starting on Monday, known as "general congregations", set the date for the start of the conclave and help identify candidates to be leader of the world's 1.2 bilion Catholics.
The Vatican is now expecting 115 "cardinal electors" - cardinals aged under 80 - to attend the conclave after O'Brien opted out and an Indonesian cardinal said he was too sick to attend.
The field for next pope remains wide open, with possible candidates from every corner of the world and from both progressive and traditionalist wings of the Church.
The pre-conclave meetings, which are expected to last for most of the week, are also a way to identify what the priorities for the next pope should be.
Benedict's eight-year pontificate was often overshadowed by Vatican intrigue and scandals in Europe and North America over sexual abuse by paedophile priests going back decades and the cover-up of those crimes by senior prelates.
Church leaders are also concerned about issues like priestly celibacy, treatment of gays, attitudes towards divorcees, the Catholic stance on contraception as well as inter-religious dialogue, particularly with Islam.
Benedict's effort to revive faith amid rising secularism is also crucial.
"We will confront the most important issues: evangelization and the new evangelization of lands with a Christian tradition," Colombian cardinal Ruben Salazar Gomez told Italian daily Corriere della Sera on the eve of the meeting.
Honduran cardinal Oscar Andres Rodriguez Maradiaga said there would be no avoiding the issue of "Vatileaks" - a series of leaks of confidential documents last year that revealed intrigue in the government of the Church.
"We have to be informed about things that, because of the distance, we have little information about," Maradiaga told Italian public channel Rai Due.
No date has yet been set for the election of the Church's 266th pope, although Italian media have mentioned next Monday, March 11 as a possibility.
The dean of the college of cardinals, Angelo Sodano, has stressed that the start date will not be set until all the "cardinal electors" are in Rome.
The closed-door "general congregations" will also make preparations for the vote itself by, for example, ordering a special stove to be set up in the Sistine Chapel to burn ballots after each of the two daily rounds of voting.
If the smoke from the ballots is black -- a special chemical component is added -- that indicates no candidate has won the two-thirds majority required.
If the smoke is white, it means a new pontiff has been elected.
The profile of an ideal candidate for pope is beginning to come into focus as cardinals have their say -- many would prefer a relatively youthful, pastoral figure who can help foster spiritual renewal, particularly among young people.
"When John Paul II died in 2005, everyone had been thinking about a successor for months and the conclave was short," a retired cardinal told AFP.
"This time the unprecedented move of a pope resigning has upset all the calculations," he said, adding that he believed a "bold decision" like the unexpected election of Polish Karol Wojtyla in 1978 is a distinct possibility.
Among the leading candidates this time around are Italian cardinal Angelo Scola, a big promoter of inter-religius dialogue, and Austria's Christoph Schoenborn, a former student of Benedict's with strong progressive ideas.
US cardinal Sean O'Malley, who cracked down on the problem of sexual abuse in the Boston archdiocese where the scandals began to emerge, and Timothy Dolan, the gregarious archbishop of New York, are also seen as possibilities.
Canadian Quebecois cardinal Marc Ouellet, a conservative with ties to Latin America, is also highly rated.
For Latin America - home to most of the world's Catholics - Brazilian cardinal and Sao Paulo archbishop Odilo Scherer is seen as a favourite.
In Africa, Ghana's Peter Turkson, Guinea's Robert Sarah and South Africa's Wilfrid Napier, the archbishop of Duran, are also seen as possibilities.
For Asia, the most frequently mentioned candidate is Manila archbishop Luis Antonio Tagle, a 55-year-old theologian and pastor who is hugely popular.