EasyJet and Lufthansa have both submitted offers to buy parts of ailing Alitalia.
The German carrier said it hoped to establish a “new Alitalia”, but was only interested in parts of the existing business.
EasyJet said it had submitted an expression of interest but also only wanted “certain assets of a restructured Alitalia”.
The UK budget carrier added: “There is no certainty at this stage that any transaction will proceed and easyJet will provide a further update in due course if and when appropriate.”
Both airlines are also bidding for parts of bankrupt Air Berlin.
Alitalia said it had received seven offers by a 5pm deadline on Monday and would now assess them.
The Italian government has postponed the deadline for making a final decision over the Alitalia sale from November 4 to April 2018.
The government also announced a further €300 million in loans on Friday to keep the carrier flying.
Rome has already provided €600 million in funds since May, but has now extended the repayment deadline to September 30 next year, following the decision to delay completion of the sale.
Alitalia went into administration in May after staff rejected job and salary cuts as part of a €2 billion rescue plan.
Lufthansa said it was interested in “parts of the global network traffic and European and domestic point-to-point business”.
Italian newspaper Corriere della Sera, referring to anonymous sources, said on Monday that the Lufthansa bid was worth €500 million, but was likely to be rejected as the authorities in Rome wished to sell the airline’s assets as a complete package.
The newspaper reported Lufthansa was bidding for aircraft, airport runway slots and air crew and was proposing to halve Alitalia’s workforce of 12,000 staff as well as reducing its short- and medium-range flights.
Irish budget airline Ryanair expressed early interest in Alitalia but withdrew amid its pilot holiday rota crisis two weeks ago, which led to the cancellation of flights for about 700,000 passengers.