The conditions, including the ousting of Alitalia's board of directors and a vast debt restructuring plan, were presented to Italy's transport minister Maurizio Lupi some 10 days ago, Il Sole 24 Ore said, without citing sources.
The job losses are far greater than those tabled by the Italian airline in its current restructuring plan, the report said. Alitalia has been trying to persuade shareholders to inject funds as part of a €300m recapitalisation programme.
Shareholders including Air France-KLM, which currently holds a 25 percent stake in Alitalia, have until the middle of November to decide whether or not to participate in the capital increase.
Air France-KLM chief executive Alexandre de Juniac said on Thursday that since talks on recapitalisation began, the French group had been clear about requiring "strict financial, industrial and social conditions" and a "profound restructuring" for Alitalia.
The capital increase plan was put together in a hurry under pressure from the government, as energy major ENI threatened to ground the fleet by stopping fuel supplies because of unpaid debts.