Renzi's government won a vote of confidence in the Senate by 173 to 108, clearing the final hurdle for adopting the budget approved by MPs last week.
President Sergio Mattarella on Monday had asked Renzi to delay his departure for a few days to enable the budget adoption to take place.
Local news reports said Renzi may resign on Friday – Thursday being a public holiday in Italy – to give his party more breathing space. The leadership of Renzi's centre-left Democratic Party (PD) was to meet later on Wednesday.
The party is beset by internal divisions that were painfully exposed by Renzi's battle to modify Italy's constitution.
An election must be held by February 2018 but opposition parties are clamouring for it to be held up to a year early, saying the vote was effectively a vote of no confidence in the centre-left coalition.