The value of the stake up for sale was estimated at 10 trillion won ($8.9 billion), the paper said, citing unidentified industry sources.
Nexon is listed on the Tokyo stock market.
Shares of Nexon affiliates including Nexon GT Co Ltd and Nat Games Co Ltd jumped as much as 30 percent on the media report.
Deutsche Bank and Morgan Stanley have been selected to manage the sale, the report said.
Deutsche Bank and Morgan Stanley were not immediately available for comment.
The potential buyers include domestic industry rivals Kakao Corp and Netmarble Corp, as well as Chinese tech giant Tencent Holdings Ltd and U.S. video game publisher Electronic Arts Inc, the newspaper reported. citing unnamed industry sources.
"As the value of the company's stake will be enormous, there will be very limited buyers with the ability to purchase Nexon," said Oh Dong-hwan, an analyst at Samsung Securities.
NXC Corp spokeswoman declined to comment.
Nexon founder Kim Jung-ju would sell a total of 98.64 percent stake in NXC Corp held by himself and related parties including his wife, according to the media report.
($1 = 1,121.5000 won)
(Reporting by Heekyong Yang; Editing by Richard Pullin and Stephen Coates)