In the previous round of auction, Korean Air Lines was the sole preliminary bidder, but the country's national security laws requires submission of two or more bids for the sale to proceed.
Hyundai entered the bidding after a shareholders' plan to sell a stake in KAI failed in August due to lack of bidders.
"Hyundai Heavy Industries intends to enter into the aeroplanes manufacturing business as it has seen slump in orders for commercial ships."
State-run financial institution Korea Finance, which is in charge of the sale process, said that the bidders would be allowed to conduct due diligence in October and submit binding bids in November so that the deal can be closed by the end of the 2012.
Korea Finance is selling 26.4% stake, while Seoul-based multinational automobile company Hyundai Motor, Seoul-based conglomerate company Doosan Group and automation and weapons technology company Samsung Techwin are selling the remaining equity in the aircraft manufacturer.
The 41.75% stake is estimated to be KRW1.13trn ($1.02bn).
In early 2012, each of these shareholders put up about 10% of their stake for sale, which also included management control.
Korean Air Lines already manufactures parts for several aircraft programmes and offers MRO services for commercial and military planes.
KAL and Hyundai Bid for Korea Aerospace
Korean Air Lines and shipbuilding company Hyundai Heavy Industries have both made bids to acquire a 41.75% stake in Korea Aerospace Industries (KAI).