"We are working. I was optimistic yesterday, I am optimistic today," said Italian Transport Minister Maurizio Lupi after another round of crisis talks ended on Tuesday without a solution.
First on Alitalia's alarmingly long list of problems is a threat by Italy's oil giant ENI that kerosene supplies will be shut off if bills are left unpaid.
ENI "cannot provide credit to a company whose future seems no longer assured," said the firm's chief executive Paolo Scaroni on Tuesday.
"If Alitalia doesn't get the support of its shareholders, we cannot keep it alive with our gas," ENI's chief said.
According to local news agencies, Italy's aviation authorities are expected to assess Alitalia's ability to continue as a viable company in the coming days, with the recourse to bankruptcy proceedings on the table.
Only the arrival of fresh capital from shareholders or banks can stop the flagship carrier from entering receivership, an Alitalia executive who wished to remain anonymous said.
Alitalia has not made a profit in years, and in September posted net losses of €294 million for the first half of the year.
With its results, Alitalia called for a capital increase of €100 million, but only a handful of the company's 20 or so shareholders were ready to pay. Crucially, biggest shareholder Air France-KLM resisted the call.
Air France-KLM took a 25-percent stake in Alitalia in 2008 in a compromise deal. The Franco-Dutch group had wanted to buy its struggling Italian rival, but the proposed takeover was blocked by former prime minister Silvio Berlusconi.
On Sunday, Italy's current Prime Minister Enrico Letta said that decision was an error "that we are paying for today".
The price of the error could be huge, with Alitalia employing 14,000 people.
A proposal in crisis talks chaired by Letta on Monday to corral Italy's national rail company into helping was reportedly dropped.
This leaves Air France-KLM as the only likely saviour, but the group has problems of its own, and this week announced a huge restructuring involving about 1,800 lost jobs.
"Our conditions for helping Alitalia are very strict," Air France chief Alexandre de Juniac told Les Echos newspaper last week.
"If the conditions are not there, we won't be able to do it."
Alitalia's board of directors were set to meet later Tuesday ahead of a shareholder meeting on October 14th.
Don't want to miss a story about Italy? - Then join The Local Italy on Facebook and Twitter.