"If one or more political forces adhere to my agenda and put forward the idea of proposing me for the post of premier, I would weigh the option," the outgoing premier said at a news conference following his resignation on Friday.
Monti cannot officially be on the ballot for the February 24-25 vote as he is already a senator-for-life but under Italy's electoral system he could be asked to join the government, even as prime minister, by whoever wins.
"I am ready to give my approval, my encouragement and, if called to, my leadership" to those parties who get behind the reforms, Monti said.
Monti outlined a programme to "change Italy and reform Europe", saying that the main point was not to turn the clock back on austerity measures and reforms and thereby "destroy the sacrifices that everyone has made this year".
A former economics professor and high-flying European commissioner, the 69-year-old urged more reforms of Italy's "archaic" labour laws, an overhaul of the painfully slow justice system and more equal opportunities for women.
Monti also took on billionaire media tycoon Silvio Berlusconi, saying that his predecessor, who is running in his sixth election in two decades, had made proposals including the abolition of a new property tax that were "very dangerous and illusory".
Monti defended his record after 13 months in government, saying Italy -- battling a two trillion euro debt mountain -- had managed to extract itself from the eurozone debt crisis without resorting to an international bailout.
"The financial crisis has been overcome," he said.
Monti handed in his already announced resignation on Friday after Berlusconi's People of Freedom party withdrew its support for his technocrat government in parliament, triggering early elections.
That could turn the February vote into a nail-biting three-way race between the scandal-tainted Berlusconi who has dismissed Monti as "a complete disaster", former communist Pier Luigi Bersani and a Monti-backed reform coalition.
Other options mentioned by local media in recent days include the possibility that Monti could take on the largely ceremonial role of president, who is elected by parliament, or a top post in the European Union.
Opinion polls have so far tipped Bersani and his Democratic Party as the winners of the election but without an outright majority, which would require a coalition.
Bersani has said he will follow the broad course of reforms set by Monti but will face trade union pressure to moderate draconian austerity measures.
Berlusconi remains a formidable campaigner and could benefit from a vote split between the centre and the left.
Berlusconi, who was convicted of tax fraud in October and is currently on trial for having sex with an underage prostitute and abuse of power, has begun a strident campaign against Monti's economic policies and his possible bid for office.
He said Monti risks being "the little leader of a little party".
European leaders and Italian businesses have urged Monti to stay on, saying he has given Italy unprecedented stability at a particularly turbulent time.
He has also received the endorsement of the Roman Catholic Church, which is an influential political player in Italy and is wary of a leftist government that could back gay marriage and is also now virulently against Berlusconi.
But while Monti's austerity and bold economic reforms have received wide praise from investors and have rescued Italy from the brink of bankruptcy, they are increasingly unpopular among Italians who have been on the receiving end.
Monti's ratings have plunged from more than 60 percent shortly after he took over in November last year to around 30 percent in recent weeks.
Some observers say he is unwilling to risk losing the respect he has earned abroad and the cross-party appeal he has built up in 13 months in government by entering a messy election battle.
Another development to watch in the elections will be the rise of far-right and Eurosceptic movements that have tapped into rising social anger.
The populist Five Star Movement led by former comedian Beppe Grillo is also expected to do well, based on its anti-corruption, pro-environment campaign.