Alitalia, which has made a profit only a few times in its 70-year history, was put under special administration earlier this year after staff rejected a plan to cut jobs and salaries.
Seven envelopes were delivered by a deadline to submit binding offers for parts or all of the airline on Monday, Alitalia said in a statement, but gave no further details.
It was unclear whether any of the offers were for the whole airline. Both Lufthansa and easyJet said they were only interested in parts of it.
This may not find favour with Rome, which wants to sell the airline in one block to minimise the impact on its 12,000 staff.
Rome has ruled out renationalizing Alitalia, an airline that was once a symbol of Italy's post-war economic boom but is now struggling to compete at home against low-cost carriers and high speed trains, and has not invested sufficiently in the higher-margin long-haul routes to get back to profit.
Lufthansa did not provide details of its offer but said it included plans for what it termed a new Alitalia "which could develop long-term economic prospects".
Italian newspaper Corriere della Sera reported Lufthansa was offering 500 million euros ($590 million) to acquire the planes, airport runway slots and air crew. Citing three anonymous sources, the paper said it also proposed halving Alitalia's workforce.
easyJet said it was interested in "certain assets of a restructured Alitalia" but gave no details.
Low-cost rival Ryanair had also been interested, but pulled out to focus on its rostering issues.
The bidders have until April 30 to improve their offers. After that the most suitable offer will be put forward for regulatory and anti-trust approvals.
The process was expected to be wrapped up in November, but was extended last week, raising questions over the likelihood of a deal coming through quickly, especially with Italy gearing up for a general election early next year.
The government also added a further 300 million euros to the loan of 600 million euros it gave Alitalia in May.
"The delays and additional government handouts only show Alitalia keeps burning cash and cannot be easily restructured, and its negotiating power only weakens as time passes," said Andrea Giuricin, transport expert at Milan's Bicocca university and author of "The endless privatisation of Alitalia".
"Come next year Alitalia will again become a pawn in the election game."
Alitalia remains a political hot potato for Rome, and any tough restructuring of the carrier to suit a foreign investor would rankle. It also remains to be seen how committed any of the bidders are to see a deal go through.
The offer from Lufthansa, which also owns Brussels Airlines, Swiss, Austrian and Eurowings, comes after it agreed a deal last week for large parts of Air Berlin
This raised concerns whether an additional move for Alitalia "would be a deal too far with regards management focus and capital needs", Goodbody analysts said in a note.
($1 = 0.8481 euros) - Reuters