One senior airline official told journalists on Sunday that "Olympic has reached a bottleneck".
It has been known for some time that the carrier has a crippling debt, but up-to-date figures are not available.
In 2000, the last year for which the state-owned airline bothered to publish annual results, its accumulated losses totalled a staggering $407.1 million dollars.
The airline, founded in 1956 by Greek tycoon Aristotle Onassis, is not believed to have made any dramatic profitability improvements after a global downturn in ticket sales after 11 September and the SARS outbreak.
In fact, Olympic debt has reached Olympian proportions after the European Commission began nipping at its heels.
Brussels announced in December it had fined the airline over $200 million for misusing and illegally obtaining state support. Greece said it would appeal the decision.
Greek Transport Minister Christos Verelis signaled significant change last Thursday.
He announced that a slimmed-down version of Olympic would start operating in September.
In the coming days, the Greek parliament will pass a law separating OA's flight activities from its non-flight operations, such as maintenance and ground handling, he added.
The sale of non-flight operations is expected to finance the "New Olympic's" ongoing expenses until new owners are found, according to Verelis's plan.
Among the non-flight assets on sale are ground handling operations, technical maintenance facilities and a kerosene delivery company.
The government hopes a revamped airline will be easier to sell to private investors.
A series of past attempted sell-offs hit the wall, the most high-profile one when a rival carrier, which had been declared as preferred bidder, flew into bankruptcy itself before he had the opportunity to save Olympic.
Flights-related staff is to be slashed to about 1,800 employees, down from the current 2,250. Olympic officials aim at cutting the airline's motley fleet down to two types of aircraft, notably Boeing 737s and Airbus 320s.
Potential private owners are to buy the company's trimmed labour force, a logo resembling the Olympic Games' six rings and the wholly owned planes of OA's 44-strong aircraft fleet.
"I think sale conditions are much better now. The government decided to do the cleanup first before selling the airline. Now it's much clearer what's at sale," Christos Stamoulis, president of Olympic's pilot union EHPA, told AFP.
The European Commission seems to be giving Greece the breathing space needed to come up with a solution. It has not yet appealed to the European Court of Justice to enforce its 194-million-euro fine.
In a report issued in the mid-1990s, the commission spoke of "management errors, lack of any system of internal controls (and) the imposition of public service obligations without financial compensation".
For years on end the airline had to transport Greek government officials and journalists virtually for free.
The 2004 Athens Olympics, on which OA has paid 10 million euros in free tickets to become the Games's official carrier, may offer the airline a glimmer of a chance to regain some of its past shine.