Advertisements appeared in four newspapers offering all or parts of the carrier for sale.
The notices were placed by Augusto Fantozzi, the commissioner appointed after the airline went into receivership late last month.
They called for "whoever might be able to guarantee the continuity, in the medium term, of the transportation service ... to submit its expression of interest."
The notices appeared in three Italian newspapers - Corriere della Sera, il Sole-24 Ore and la Repubblica - and the London Financial Times.
If no buyer comes forward, Alitalia, which is losing ”2m (”1.6m) a day, is likely to shut down next Tuesday, October 1.
One creditor, the Israeli Airports Authority, has already begun moves to recover money allegedly owned to it.
But there was a glimmer of hope that the airline might be saved after the right hand man of prime minister Silvio Berlusconi was reported by Reuters as having had talks with the consortium today (September 24).
Reuters also reported that Mr Berlusconi had cancelled his visit to the United Nations General Assembly in New York because of the crisis over the airline.
Mr Fantozzi made his move after the latest attempt to save the carrier failed.
He had already threatened to ground the airline and terminate contracts if agreement to sell could not be reached.
A 16-strong consortium, CAI had bid ”1bn for the carrier but failed to reach agreement with all nine unions at Alitalia.
Under the proposed deal, the Italian government would sell its 49.9% stake to CAI which would then merge the profitable parts of the carrier with rival Air One.
The unprofitable parts would be liquidated by the government.
But the plans would have entailed 3,000 job losses which many of the unions refused to accept.
Maurizio Saconni, the Italian labour minister, said that all possible airlines which might be interested had now turned down the chance to take over the carrier.
This included Air France KLM whose own takeover attempt earlier this year was rejected by the unions.