The 133 cardinals are holding near-daily meetings to discuss issues facing the 1.4-billion-member Catholic Church before Wednesday's conclave, when they will be sequestered in a hotel and barred from contact with the outside world.
While there are a few cardinals seen as frontrunners to succeed Pope Francis -two often mentioned are Italian Cardinal Pietro Parolin and Filipino Cardinal Luis Antonio Tagle - many of the clerics who will vote have not made up their minds.
"My list is changing, and I think it will continue to change over the next few days," British Cardinal Vincent Nichols, participating in his first conclave, told Reuters. "It's a process which for me is far from concluded, far from concluded."
As the cardinals are meeting this week in what are called "general congregations", individual clerics can offer speeches to give their vision for the future of the global faith.
During the 2013 conclave, it was in this period that Argentine Cardinal Jorge Mario Bergoglio gave a speech that, by many accounts, deeply impressed his peers. Days later, he was elected as Francis.
Nichols, the highest-ranking church official in England and Wales, said the speeches this time have again been pivotal in helping form opinions about who could be the next Pope.
"There'll be these moments when like a stone is dropped into a pond and the ripples will go out and I'll sit there thinking, 'Ah, yeah, that's important,'" said the cardinal.
Asked about whether there are cardinal frontrunners who are more likely to become pope, Nichols replied: "I came with a few ideas ... (and) they have changed."
Cardinal William Goh Seng Chye, the archbishop of Singapore, told Il Messaggero newspaper he also did not know who the next Pope might be.
"It may seem strange, but we really do not know," he said. "We have not yet begun to vote, so we don't know. The game is still going on."
The cardinals were meeting for two pre-conclave sessions on Monday and are expected to have at least one more on Tuesday.
The conclave itself begins on Wednesday morning local time (Wednesday evening AEST) with the celebration of a special mass in St Peter's Basilica.
In the afternoon, the cardinals will formally process into the Sistine Chapel, the storied 15th-century worship space adorned with frescoes by Michelangelo, where they will begin voting for the next Pope.
They are expected to take one vote on Wednesday afternoon. Subsequent days will have two votes each morning and afternoon. It takes a two-thirds majority for someone to be elected.
According to conclave regulations, if no one has been chosen after the first three days, the cardinals should take a day-long "pause of prayer" before continuing.
The only signal given to the outside world about the deliberations will come from a chimney installed above the chapel.
The cardinals will burn their ballots, adding a chemical product to create one of two colours of smoke: black for an inconclusive vote; white when there is a new Pope.
Italian Cardinal Fernando Filoni, a former Vatican official participating in his second conclave, told Corriere della Sera newspaper he expected the first votes to be indecisive.
"The first two votes are for orientation, then we start to sum things up," he said.
