"It is an important test for Matteo Renzi - he needs to find a name capable of securing the broadest possible backing," analysts at the Unicredit bank said in a note to investors on the selection procedure for a successor to the much-loved and respected Giorgio Napolitano.
A total of 1,009 politicians have a vote on who takes over the largely ceremonial role, with the members of the Chamber of Deputies and the upper-house Senate joined by 58 representatives of Italy's regions in a first vote scheduled for 1400 GMT.
A new president is seen as unlikely to emerge from the first three rounds of voting, in which, constitutionally, a two thirds majority is required. From the fourth round, a simple majority is enough. Renzi's ruling Democratic Party (PD) can officially count on 415 votes from its own elected officials and several dozen floating voters.
As a result, Renzi is counting on being able to ensure his favoured candidate carries the day in the fourth round, which will likely happen on Saturday, and has reportedly ordered his loyalists not to vote at all in the first three rounds.
No clear favourite has emerged from weeks of wheeler-dealering in the wake of the 89-year-old Napolitano's decision to stand down mid-way through his second term.
"Negotiations have run into the sand amid a game of veto and counter veto," observed the daily Corriere della Sera.
'Politician not technocrat'
The influential broadsheet suggested Renzi was playing his cards close to his chest because "he doesn't yet have a solution at hand," amid delicate negotiations with Silvio Berlusconi, one of his predecessors and the man who wields the most votes on the other side of parliament.
Paolo Romani, one of Berlusconi's right-hand men, said efforts to reach a consensus on the new president had advanced little beyond agreement that it should be a high-profile figure and a "politician rather than a technocrat."
Luigi Di Maio, a senior official with the populist Five Star movement which is backed by around one in five Italian voters, described Renzi's maneouvring around the presidential vote as worthy of the KGB.
Renzi aides insist the uncertainty is due to the absence of a candidate who is clearly capable of uniting the premier's own - sometimes unruly - troops and securing enough cross-bench backing to command a majority.
"Even if the papers produce a 'sure' name every day, there still isn't one nbecause we decided to find the name together," Renzi said on Wednesday.
According to the press, the frontrunners are all men, despite opinion poll evidence that many Italians believe it is about time a woman was given the role.
Former premier Giuliano Amato, current finance minister Piercarlo Padoan and constitutional judge Sergio Mattarella are all seen as being in with a serious shot, with Renzi said to be leaning towards Mattarella.
Potential dark horses who could emerge at the final moment are said to include Senate speaker Pietro Grasso and anti-corruption Tsar Raffaele Cantone.