Aigle Zur, which employs almost 1,200 staff, filed for bankruptcy and suspended flights last week after losses which prompted a shareholder coup that ousted the chief executive.
The French secretary of state for transport, Jean-Baptiste Djebbari, told Le Parisien daily there were still 13,000 passengers "in difficulty", only slightly down from 19,000 when the crisis began.
He said these included 11,000 passengers booked on flights into and out of Algeria, 600 on Mali flights as well as other destinations ranging from Russia to Lebanon.
Aigle Azur operates 11 planes but unions say potential suitors are likely to be most interested in its landing slots at the busy Paris Orly airport, the second biggest hub in the French capital in the south of the city.
The head of the Aigle Azur branch of the French pilots' union SNPL, Martin Surzur, said after meeting Djebbari in Paris that two serious offers had been received from potential buyers.
An Air France spokesperson confirmed to AFP that the company had made an offer, without giving further details. The identity of the other potential buyer has yet to be made clear.
The airline transported last year some 1.9 million passengers, with destinations in Algeria making up half of its operations that brought in 300 million euros ($329 million) of revenue.