An Air One takeover would keep Alitalia in Italian hands but there has been doubt over whether the smaller airline has the wherewithal to turn around an airline with a long list of woes.
The Air France-KLM choice would make Alitalia part of the world's biggest airline by sales but at a sharp discount to its share price and with potentially unpalatable job cuts.
The Franco-Dutch airline's proposal will be well below Alitalia's market value of 1.1 billion euros, a source familiar with the matter said. Air France-KLM has emphasised it would not do a deal that would dent its profitability.
Alitalia also has about 1.2 billion euros of debt.
Shares in the Italian airline jumped more than 6 percent to a one-month high after Air France-KLM said it was sending a non-binding letter of interest to the company's board, and were up 3.25 percent at 0.87 euros in afternoon trade.
More details about the offers could come after Alitalia's board meets at 5 pm London time. Alitalia is expected to pick a bidder in mid-December with which to start exclusive talks.
Air One said it would make an offer before Thursday's deadline. It is the only name left from an earlier attempt to auction Alitalia and is backed by bank Intesa Sanpaolo.
Air France-KLM said it aimed to develop a business plan in line with Alitalia's latest "survival" plan unveiled in August that would scale back the airline's presence at Milan and focus on its Rome hub.
It said it would be "counting on the support of the Italian carrier's entire workforce." Alitalia is infamous for its strong labor unions that have staged crippling strikes to thwart management efforts to cut jobs.
The airline said an Alitalia bid would also meet the requirements for its economic and financial stability, but said it continued to also weigh an offer for Spain's Iberia.
Air France has been tipped as a suitor for Alitalia since a marketing agreement struck in 2001 and a share-swap deal the following year. But it played down talk of a bid over the past year, saying Alitalia should first sort out its problems.
Italian Prime Minister Romano Prodi has said Alitalia should go to the best bidder, with Italian ownership a secondary issue.
Lufthansa shares were up 1 percent at 18.39 euros, reversing losses after the company said it would not bid for Alitalia.
Shares in Air France-KLM were up 2.5 percent at 23.83 euros after touching 24.65 earlier in the session.
Lazard is advising Air France-KLM.