Renzi, the new leader of the Democratic Party, has been in talks with allies to create a new left-right coalition cabinet for the past two days, the Wall Street Journal reported Friday.
Angelino Alfano, head of the New Center Right party, which broke away from Silvio Berlusconi's Forza Italia, was also present for the talks.
"I think we'll close [the ministers list] today," said Lorenzo Guerini, spokesman for the Democratic Party's leading team.
After the list is completed, Renzi will present it to Napolitano before the cabinet is sworn in by the Italian Parliament, a ceremony that could take place as soon as Monday.
Last week, Renzi, 39, led a revolt, forcing his predecessor, Enrico Letta, to resign from office.