US private equity group Cerberus Capital Management has approached Alitalia with an offer that would allow the carrier to remain independent, according to the Financial Times.
Cerberus told Alitalia that it was still interested in buying the airline if it could be comprehensively restructured, the FT said, citing sources.
Germany's Lufthansa and British budget airline EasyJet were among the seven bidders for Alitalia, in a formal sale process last week.
Both Lufthansa and easyJet had said they were only interested in parts of the carrier.
New York-based Cerberus had decided against submitting its own offer as it considered the terms of the public tender too restrictive, the newspaper said.
Cerberus suggested it would be willing to invest funds worth somewhere in the "low nine-digits", or between €100-400m, to gain control of Alitalia, the newspaper said.
It also planned to ask the Italian government to retain a stake in the airline, with trade unions benefiting from some form of "profit sharing", the FT said.
Cerberus has also offered to "step in" to get a "head start" on reorganising Alitalia without charging any fee, even before making its investment, the newspaper said.
The ailing airline, which has made a profit only a few times in its 70-year history, was put under special administration earlier this year after its staff rejected a plan to cut jobs and salaries.