Fosun is one of six candidates shortlisted by the family controlled Forbes group’s bankers, according to the Financial Times.
The Hong Kong-stock market-listed Fosun publishes the Chinese version of the magazine.
Bids may run to some $475 million, and the Wall Street Journal reports that Fosun may bid in partnership with another firm called G2 Whale Capital.
Fosun has a wide range of investments spanning industrial, pharmaceutical and media sectors. It recently bought Portuguese insurer Caixa Seguros and is also said to be nearing a deal for travel group Club Med.
Its media interests include a 6% stake, bought last September, in NASDAQ-listed mainland Chinese producer-distributor Bona Film Group.
Earlier this month it emerged that another Chinese billionaire Chen Guangbiao is having a tilt at buying the New York Times from its family owners.