A move toward privatization will likely depend on several factors that must be resolved before any actual bidding begins:
Overstaffing, under working and underperforming, both on the ground and in the air. The new owners must get clear title to reduce, upgrade, re-train and transfer staff, as necessary.
Establishing the relative value of all assets: aircraft, routes and landing slots, ground operations. These may be valued together, as a package, or broken up and sold separately.
Withdrawal of Aerolíneas’ monopoly on certain internal and external routes.
Clean up the balance sheet to reveal the full amount of debts and future obligations, including the costs of making a portion of staff redundant, bringing aircraft up to standard, paying off any loans to the state, etc.
Once all those numbers are clear, published and agreed, both inside and outside Argentina, then the privatization process can proceed substantially as similar processes took place in Europe after the Maastricht Accords.
In Spain, for example, the government convinced / pressured certain solvent, national entities (banks, department store chain El Corte Inglés, the national, industrial holding company SEPI), to take large shareholdings in the newly privatized Iberia. Free floating shares were limited, ensuring stability and government cooperation. The privatization was successful with later entry of British Airways and American Airlines into Iberia.
That kind of scenario assumes that all will go well. If it does not, and Milei is true to his word, if a buyer(s) (including joint venture partners) cannot be found then the airline would presumably fold, as was the case in Europe with Olympic Airways (Greece), Sabena (Belgium) and others.
This is just speculation, drawing from a bit of history. And Aerolíneas is just one of at least 41 (some sources say 60), state-owned enterprises that Milea has promised to privatize. The likelihood of its getting special treatment is slim. As always, the devil is in the details, and Aerolíneas’ pilots’ and crews’ unions have already announced that they are strongly against any sort of privatization.