Korea Aerospace Industries' (KAI) share sale could be scrapped as only one party has expressed interest.
The deadline for the submission of letters of intent was 16 August, but the firm will accept bids from now until the end of the month.
To comply with the country's laws, however, the sale will be called off if fewer than two bids are submitted, says a KAI spokesman.
Following that, KAI's shareholders could try selling the shares again next year, he adds.
Korean Air is the only company to submit a letter of intent to bid for a stake in the aircraft manufacturer.
KAI announced on 31 July that six of its shareholders are offering to sell a combined 41.75% stake in the company, 11.4% of which comes from state-owned Korea Finance Corporation.