Big conglomerates GS, SK and Hanwha would not participate in the bidding for the debt-ridden carrier, company spokesmen said.
The 31.05% stake, worth 387.4 billion won ($319.5 million) as of Monday's closing price, has been put up for sale by top shareholder Kumho Industrial, which has been under pressure from creditors to reduce its debt.
The sale comes as the South Korean airline industry struggles with higher fuel costs and weakening demand due to a diplomatic row between Seoul and Tokyo.
Asiana Airlines and bigger rival Korean Air Lines swung to operating losses for the April-to-June quarter, from a year earlier.
KCGI would form a consortium to bid for the Asiana stake, a KCGI source said without disclosing its partners.
South Korean brokerage Mirae Asset Daewoo also would take part in the deal as a financial investor, a company official said without elaborating.
Asiana shares rallied more than 7% on Tuesday, while its budget arm Air Busan and Asiana IDT gained more than 4% each.
(Reporting by Hyunjoo Jin and Ju-min Park; editing by Richard Pullin and Stephen Coates)