Italy's President Giorgio Napolitano has asked Matteo Renzi, the mayor of Florence, to form a new government, BBC reported.
Enrico Letta resigned as prime minister on Friday, after he was ousted in a vote called by Mr Renzi at a meeting of their centre-left Democratic Party.
Mr Renzi, who has never been elected an MP, will now have to come to a deal with Mr Letta's former coalition partners.
He could be sworn in on Thursday, reports say.
Mr Renzi would become Italy's youngest ever prime minister, two months younger than Benito Mussolini when he came to power in 1922.
In a separate development on Monday, Italy's borrowing costs dropped to their lowest rates for almost eight years. Ten-year debt bonds fell to 3.64%, seen as an apparent nod from the markets towards Mr Renzi's plans for economic reform.
Mr Renzi, the Democratic Party leader, spent more than an hour in talks with President Napolitano in Rome on Monday morning. Party colleague Maria Elena Boschi said it would take several days to form a new administration.
After being sworn in by the president, he would need to win votes of confidence in both houses of parliament.
Mr Renzi, 39, helped to engineer Mr Letta's ousting as prime minister after questioning the performance of his coalition government and accusing him of failing to implement promised reforms of what is seen as an often corrupt and wasteful bureaucracy.
The ex-prime minister had come under increasing pressure over Italy's poor economic performance and Mr Renzi argued that a change of government was needed to end "uncertainty".
Mr Letta's position became untenable once the Democratic Party backed a call for a new administration.
He only lasted 10 months in post after forming a coalition government with the centre-right last year.
Mr Renzi's initial priority will be to secure the support of the small New Centre Right (NCD) party in order to command a parliamentary majority and start cabinet building.
So far, the leader of the centre-right faction that formed the previous coalition with the Democratic Party and the centrists has given a guarded response to Mr Renzi's plans.
Angelino Alfano warned that the coalition remaining intact was "not a given" and told his party supporters he would demand promises from Mr Renzi before joining the new government.
"We are decisive for the creation of the new government. If we say no to this government, it won't come to life," he said. Italian media report that the two men have been in regular contact by text message over the weekend.
The mayor of Florence has never been elected to parliament or served in government before and is viewed by many as an outsider.
The BBC's Alan Johnston says Italy is desperate for political change and Mr Renzi's youth and dynamism, and his talk of the need for sweeping reform, have propelled him to the centre of the national stage.
Democratic Party Senator Roberto Cocianich told the BBC that Mr Renzi had attracted widespread backing: "He is supported by many entrepreneurs, for instance the leader of the entrepreneurs union and by the unions as well."
However, in an apparent setback for Mr Renzi, a leading Italian businessman, Andrea Guerra, turned down the offer of a post in his government as economic development minister.
Mr Guerra, chief executive of the world's biggest eyewear company, Luxottica, wished Mr Renzi all the best in his efforts to form an administration but said he was needed by his company.
Rai TV reported that Emma Bonino was likely to be asked to remain as foreign minister.
Once he has formed a government, Mr Renzi will have to return to the president for his nomination to be confirmed and will then be sworn into office.
Then, in order to win the support of both houses of parliament, Mr Renzi will need the support of senators and deputies in both the NCD and the centrist Civic Choice, the former party of ex-PM Mario Monti, as well as other smaller parties.