Shares of the carrier slid nearly 5.2% and those of its low-cost arm, Air Busan Co Ltd, ended nearly flat, as the company attracted no bids from major funds and larger conglomerates like SK Group and GS Group.
South Korean airlines have struggled with losses and debt amid rising competition from budget rivals, falling tourism traffic between South Korea and Japan, higher fuel costs and unfavourable currencies.
The 31.05% stake, worth about 365 billion won ($315.28 million) at current prices, was offered for sale by top shareholder Kumho Industrial Co Ltd as it struggles to reduce debt. The price is expected to grow sharply, as the buyer will also take on new shares issued by the loss-making carrier, plus a premium, analysts say.
The other two bidders are a consortium of Hyundai Development, brokerage Mirae Asset Daewoo and activist fund KCGI, which partnered with BankerStreet for the bid.
It will take about a week to choose a preferred bidder, top shareholder Kumho Industrial said, although that schedule could change.
"We aim to name the preferred bidder as soon as possible and close the deal accordingly," it said in a statement.
Kumho Industrial in April hired Credit Suisse to manage the sale of its stake.
Aekyung Group, which controls South Korea's top budget carrier Jeju Air, said acquiring Asiana would allow its airlines to achieve economies of scale and reduce redundancies.
Shares of AK Holdings, the holding firm Aekyung Group, rose as much as 13%.
(Reporting by Heekyong Yang and Hyunjoo Jin; Additional reporting by Ju-min Park; Editing by Muralikumar Anantharaman, Stephen Coates and Gerry Doyle)
By Heekyong Yang and Hyunjoo Jin