Gabriele Del Torchio told unions that “nobody will be fired” as the airline seeks to cut €128 million from its labour costs, La Repubblica reported.
He said the savings will instead be made by cutting certain benefits and through a “solidarity contribution” from those earning more than €40,000 a year.
The unions, however, are not convinced.
“The company must be willing to see us again regarding proposals to change the unions,” Claudio Tarlazzi, the secretary-general of the UIL transport union, told La Repubblica.
“The workers are the prime shareholders - they should be able to intervene and monitor the management of the company.”
In early December, Alitalia said a capital increase aimed at raising up to €300 million had attracted €173 million from shareholders at that point.
The Italian government has said the state postal service has undertaken to contribute €75 million and has denied that this constitutes state aid
The contribution is expected to help keep the airline flying over Christmas and as it seeks a foreign partner to help return it to profit.
However, analysts have warned that it may be forced to ground its fleet within six months unless a partner is found.
Alitalia has so far failed to convince its main shareholder Air France-KLM, which holds a 25 percent stake, to take part in the rescue.