Atlético chairman Enrique Cerezo will travel to Beijing this week to close the deal with Wang, owner of real estate and cinema giant Dalian Wanda, and a keen football fan, Spanish newspapers said.
Madrid sports daily AS said Wang planned to pay €40 million ($46 million) for the stake.
The club, who have had problems keeping up with growing debt in recent years despite their success on the field, declined to confirm the reports to AFP.
Various media reported that Cerezo and Wang were expected to sign the deal on Wednesday.
Atlético won last season's league title and were beaten by city rivals Real Madrid in the Champions League final.
The deal would involve opening Atlético Madrid football schools in China, sponsorship deals and a possible tour by the club to China later this year, the Spanish reports said.
Wang is number 42 on Forbes magazine's list of the richest men in the world, with a fortune estimated at $18 billion.
He was once owner of the Dalian Wanda football team in China but sold his stake in 2000 following a number of match-fixing scandals in the Chinese league. He returned in 2011 to become a sponsor of the league.
Last year he paid €265 million to buy the Edificio Espana, an iconic skyscraper in central Madrid, from Santander bank. He has also invested widely in other major European cities.
Wang raised $3.7 billion last month by floating a chunk of his Wanda stock on the Hong Kong stock market.
If the deal is confirmed, Wang would be the latest major foreign investor to enter Spain's football market.
Singapore billionaire Peter Lim recently took control of Valencia while Sheikh Abdullah al-Thani, a member of Qatar's royal family, took over Málaga in 2010.