Pro-Vatican centrists are pressing Monti to run.
Monti, an economist appointed in 2011 to save Italy from financial crisis, is a practicing Catholic whose Cabinet includes a minister closely linked to the Vatican.
Monti says he'd serve again if asked by political forces backing his austerity agenda.
Benedict's greeting to Italians Tuesday included a wish that they reflect on a "hierarchy of values" when making important choices.
The ANSA news agency says that is "very close" to a Monti endorsement for February's elections. Vatican pronouncements wield influence in Italian politics
Monti's predecessor, Silvio Berlusconi, is plagued by sex and corruption scandals.
Berlusconi, denying any wrongdoing, hasn't clarified if he's running.