Interior Minister Angelino Alfano met today with President Sergio Mattarella, who must choose a new premier.
Renzi quit after voters rejected his proposed reforms in a December 4 referendum.
With financial markets and European Union partners concerned about crises facing some Italian banks, Mattarella is expected to decide as soon as Sunday or Monday.
Renzi's Democrats are Parliament's biggest party, so Mattarella is expected to pick a Democrat to try to form a government.
Renzi and the current economy and foreign ministers are considered top contenders.
Citing Italy's economic problems, Alfano says a new government is needed rapidly.