In an advertisement placed in the Financial Times on Monday, Air Algerie invited consultants to express interest in preparing the airline for privatisation.
The Algerian government has said it wants to sell off a wide range of state assets.
But, so far, it has had little success in attracting foreign investors outside the oil and gas industry.
Air Algerie had not been mentioned previously among potential privatisation candidates.
World Bank loans
In June, the World Bank loaned Algeria $9m to assist with the privatisation of telecommunications and postal services, as well as a further $5m for unspecified privatisation assistance.
The airline said it wanted a study carried out of its present situation.
It also wanted a plan for its medium term strategy, an analysis of the possible approaches to a sale, and a recommendation of a preferred course of action.
Established in 1953 - through the merger of Compagnie Generale de Transport Aeriens (CGTA) and Compagnie Air Transport - Air Algerie became wholly owned by the Algerian government in 1972.
Its corporate ancestor CGTA had earlier been set up as a charter airline by Air France in 1946.
Air Algerie now has almost 9,000 employees and a fleet of 47 aircraft.
Boeing order
In July 1998, it placed an order with The Boeing Company of the US for six new 737-800 planes, four of which have been delivered, and three 737-600s.
The rest of its fleet is relatively old.
Although any sale of shares in Air Algerie is likely to be some time away, prospective foreign buyers might include Air France and Alitalia, analysts say.
Some liberalisation of Algerian aviation has already taken place.
A handful of small private airlines have started up in recent years.
Air Algerie asked for interested consultants to come forward by 15 January.