The caretaker PM, who took charge in late 2011, resigned after predecessor Silvio Berlusconi withdrew his support.
Italians will choose a new government in elections on 24 -25 February.
As a lifetime senator, Mr Monti cannot run for office but can take part in an election campaign and can return to the post of prime minister if asked by a party or coalition.
After 13 months in power, the former EU commissioner and distinguished economist argues that it would be irresponsible to abandon belt-tightening measures introduced by his technocrat government.
'Hierarchy of values'
L'Osservatore Romano's outright backing came two days after the Pope, in his Christmas message, urged Italians to reflect on "a hierarchy of values when making the most important of choices".
The remark was widely interpreted as coming close to endorsing the technocrat leader.
In the past, the Vatican has supported Mr Berlusconi, who gave preferential treatment to Catholic schools, says the BBC's David Willey in Rome.
It has now changed sides, clearly indicating a preference for a democratically elected Monti administration, our correspondent says.
On Christmas Day, Mr Monti sent his first tweet, calling for political renewal: "There is no point in complaining, we must commit ourselves. 'Rise up' in politics."
Political analysts have speculated whether he will head a new centrist, Catholic coalition and whether other unelected members of his caretaker government will themselves run as candidates.
But Mr Monti's return to government is far from certain.
Although Silvio Berlusconi's People of Liberty party is doing badly in the polls, the left-wing Democratic Party is in the lead and currently predicted to poll around 30% of the vote.
Pier Luigi Bersani's party was given a boost on Thursday when anti-mafia prosecutor Pietro Grasso said he would run for office under the Democratic Party banner.