Some American and other cardinals say they want to continue the pre-conclave meetings that have been going on all week for as long as it takes so they can discern who among them has the stuff to be pope and discuss the problems of the church.
Some Vatican-based cardinals, defensive about criticisms of the Vatican's internal governance that have been aired recently, seem to want to get on with the vote arguing there's no reason to delay.
"Hopefully it will be a short conclave and start very soon," Vatican-based German Cardinal Paul Josef Cordes was quoted Wednesday as telling the German daily Bild. "I would compare it with a visit to the dentist - you want to get everything over with quickly."
Once the conclave starts, there is very little time for discussion. Cardinals take two votes in the morning, two votes in the afternoon - all of them conducted in silent prayer, not chatter, amid the frescoes of the Sistine Chapel. As a result, setting the date for the start of the conclave is akin to setting the deadline for when pre-conclave deliberations effectively finish.
These discussions are designed to give cardinals a chance to get to know one another better and dive into the problems confronting the church and who among them is best suited to fix them.
On Thursday, for example, cardinals received a briefing on the Holy See's finances amid questions about the administration of the Vatican bureaucracy and continued suspicions about the Vatican bank.
As such, "it seems very normal and very wise" to wait to set the conclave date until all cardinals are confident that they're nearing an end to their deliberations, said the Vatican spokesman the Rev. Federico Lombardi.
The arrival in Rome on Thursday of Vietnamese Cardinal Jean-Baptiste Pham Minh Man, however, signaled at least that a vote could be taken on a start date now that all 115 cardinal electors are in place.
He entered the Vatican auditorium for Thursday's afternoon session without speaking to reporters. No vote on a conclave date was taken, Lombardi said.
For the fourth day in a row, discussions on Thursday included questions about the Holy See's administration and its relationships with dioceses around the world amid complaints that the Holy See doesn't communicate well, internally or externally.
The problems of the Holy See's internal governance have been a constant theme of deliberations this week as cardinals - especially from the United States - have sought information about allegations of corruption, turf wars and cronyism that were exposed by the leaks of papal documents last year.
Lombardi said the financial briefing by the heads of the Vatican's economic affairs office, the administration of the Vatican City State, and the department overseeing the Holy See's assets and personnel was designed to give the cardinals an early peek at the Holy See's financial reports, which usually come out in July.
Such a financial briefing is called for by the rules governing the period between papacies, specifically to give the cardinals a full picture of the state of the Holy See.
Lombardi refused to comment when asked if the Vatican's bank, the Institute for Religious Works, was discussed. The bank, which was created to administer the pope's works of charity, has long been the focus of scandal for the Vatican, though it has tried to clean up its reputation by submitting itself to an evaluation by the Council of Europe's Moneyval committee.
Moneyval, which helps governments adhere to internationally recognized anti-money laundering and anti-terror financing norms, gave the Holy See a passing grade in its first evaluation last summer. But the bank received poor or failing grades on a number of fronts, with its rules on customer due diligence, wire transfers and suspicious transaction reporting declared insufficient.
This week, the widely read Italian Catholic weekly Famiglia Cristiana, which is distributed free in Italian parishes each Sunday, carried an article calling for the bank to be closed on the ground that the pontificate shouldn't have direct links to the world of finance.
It argued that there are plenty of ethically minded commercial banks in Italy and elsewhere that could be trusted to manage the Holy See's assets.
"Total transparency would thus be assured and the faithful, who continue to generously donate, would know that their money given to the church ... is destined to the poor," said the article penned by historian Giorgio Campanini.
For a magazine representing the Catholic establishment in Italy to make such a call is significant, given the deference usually paid to the Holy See by the overwhelmingly Roman Catholic country.
That said, the Vatican bank has been the source of bitter battles in recent times between the Holy See and the Bank of Italy, which doesn't have regulatory control over the bank and has taken measures to strangle its financial activities in Italy.