Speaking at a press conference here Sunday, Monti said being a senator for life, he would not back any political parties, but if some forces supporting his anti-crisis "agenda" and ask him to head the next government, he would "consider it".
Monti resigned Friday after former premier Silvio Berlusconi's center-right People of Freedom party (PdL) withdrew support from the unelected government.
"Should one or more political forces, which have firmly adhered to my agenda, show the intention to candidate me as prime minister, I would consider it," he said.
The "agenda" that would at disposal of anyone will gather the recommendations that follow up with the austerity policies carried out by his 13-month emergency cabinet.
Monti said he was unable to accept an offer from Berlusconi to lead a centrist coalition.
Monti was nominated as technocratic prime minister in November 2011, after Berlusconi's centre-right coalition government fell amidst a financial and economic crisis.