Korea Development Bank, which is conducting the sale, confirmed the deal on Friday.
A source told Reuters Orix will pay about KRW 1 trillion ($913m) for the slice.
HMM and other companies have 36% of Hyundai Securities.
It is part of an assets sale intended to raise money for Hyundai group.
HMM said earlier in January that it had started receiving letters of intent from potential buyers.
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