Alitalia went into administration at the start of May after staff rejected job and salary cuts as part of a rescue plan
British budget airline easyJet and German carrier Lufthansa both said they have submitted offers for parts of Italy's ailing Alitalia.
The stricken carrier said that it had received seven binding offers in all, without providing details.
The easyJet and Lufthansa proposals will spark disappointment in Italy, which wants to sell Alitalia in one package to avoid mass job losses.
The Lufthansa Group said it was after "only parts" of the global traffic network as well as European and domestic point-to-point business of the national carrier, which it would use to establish a "NewAlitalia".
EasyJet said it too was interested "in certain assets of a restructured Alitalia", without providing details.
The budget airline said there was no certainty that any transaction would proceed.
The struggling Italian carrier received a boost Friday when Rome said it would add 300 million euros ($355 million) to a bridging loan package.
As the deadline for making binding offers expired Monday evening, the company said it had received "seven envelopes" with offers and "the Special Commissioners of Alitalia will now begin evaluating the envelopes".
The Lufthansa and easyJet interest left trade unions cold.
"Today was supposed to be a decisive day for Alitalia's future," the UGL union's secretary Paolo Capone said.
"However as one could expect, in a market of sharks, the offers made are underbids which will have a negative impact on the future employment of its workers," he added.
Alitalia, struggling to compete with low-cost rivals, went into administration at the start of May after staff rejected job and salary cuts as part of a two-billion-euro rescue plan.
In May, Rome said it would provide a 600-million-euro loan to keep the carrier's planes in the air for around six months, staving off liquidation of the flagship airline.
Irish no-frills carrier Ryanair expressed early interest but two weeks ago said it was dropping the idea as it struggles with the fallout from thousands of cancellations of its own flights owing to a pilots' shortage.