Consultations within the Democratic Party began on Thursday evening, and Mattarella has hinted that he wants a new government formed within the week.
This government would be a cross-party coalition with a mandate to update the electoral law before the next general elections - which are currently scheduled for February 2018 but could take place as early as spring next year. A return from Renzi should not be ruled out, despite his insistence in the run-up to the referendum that he did not want a role in a technical government, but here's a look at the other likely candidates.
Pier Carlo Padoan
Photo: Andreas Solaro/AFP
Currently Italy's Finance Minister, Padoan has been considered the favourite to replace Renzi as leader - but this is Italian politics, so nothing is certain. His experience includes working as the OECD's Chief Economist and as a consultant to the World Bank and European Commission, so many believe he'd be well equipped to steer the country through the economic worries it's currently facing. However, others argue that he has not taken enough action to stem the ongoing banking crisis.
Photo: Alberto Pizzoli/AFP
Another of the most-touted names, Grasso - who is not in Renzi's close circle - was among the first to meet with Mattarella on Thursday evening. The president of the Senate and anti-mafia judge previously served as Acting President of Italy for a few weeks before the swearing-in of current president Sergio Mattarella. However, his current role may act against him, as a replacement president would have to be found for the Senate.
One of Mattarella's close allies, the Minister for Infrastructure and Transport has also served as State Secretary to Renzi and is very close to the outgoing PM. The father of nine - who almost became a professional footballer - was also part of Enrico Letta's cabinet.
Photo: Vincenzo PInto/AFP
The Foreign Minister, who has formerly served as Minister of Communications, has been one of Renzi's closest allies, and is another of the favourites to replace the ex-PM. He was one of the founding members of the Democratic Party, and if he is chosen now, it's likely Renzi will continue to play a key role.
Photo: Alberto Pizzoli/AFP
Franceschini, an author and lawyer, is Minister for Culture and former Party Secretary for the PD. At 58, he's one of the younger prospective leaders but is one of the movers and shakers of the party - he served as its second leader in 2009. Over the past few days, his name has been cited more and more as a prospective replacement for Renzi.
Photo: Vincenzo Pinto/AFP
Amato is a constitutional judge, meaning he has the necessary expertise to oversee the reforms to Italy's electoral law - not to mention the fact that he has already served as prime minister twice, for nine months in 1992-3 and just over a year in 2000-1. In fact, at the end of his first period as PM, he gave a speech saying he would retire from politics permanently, and has regularly been criticized for failing to stick to this pledge.
Photo: Frederick Florin/AFP
Another of the less likely candidates is the EU Foreign Affairs chief, who moved to Brussels in 2014. At an EU Commission briefing this week, spokesperson Margaritis Schinas was asked what would happen if Mogherini left her post for a role in Rome. Relations between Renzi and Mogherini have been rocky over the years, with the latter criticizing Renzi on Twitter for a lack of foreign policy understanding, but once he became PM he was quick to appoint her Foreign Minister and campaigned hard for her to get the top job in the EU.