Alibaba is looking to buy the stake from Yunda's controlling shareholders - founding couple Nie Tengyun and Chen Liying - who own 52.19% of Yunda through their wholly owned firm Shanghai LuoJieSi Investment Management, said one of the people. At the current market price, the stake would be worth at least $790 million.
The other person said China's dominant e-commerce firm could go beyond 10% and buy up to 15% of Shenzhen-listed Yunda.
The people declined to be identified as they were not authorised to speak with media.
Under Chinese regulations, a stake of over 5% in a domestically listed company can be sold at a discount of as much as 10% to the firm's share price on the last trading day prior to a deal.
Based on Monday's closing price, the deal could fetch at least $790 million, as Yunda has a market capitalisation of about $8.78 billion.
Alibaba has already bought a small stake in Yunda which is below threshold for disclosure, said two other people with knowledge of the matter.
Alibaba declined to comment. Yunda did not respond to a request for comment.
The move would mark another step forward in Alibaba's efforts to gain a bigger say in China's fragmented but fast-growing express delivery industry.
Domestic delivery firms dispatched 63 billion parcels last year, up 24% from 2018, while revenue grew 23% year-on-year to 745 billion yuan ($104.95 billion), data from the State Post Bureau showed in January.
But many firms are under pressure to boost logistics infrastructure and upgrade services to maintain market share as online retail continues to grow and amid continued price competition.
Alibaba's move also comes one year after it took a 14.65% stake in another large express delivery firm, STO Express Co Ltd, through a 4.66 billion yuan deal.
STO's controlling shareholder later agreed to grant Alibaba an option to purchase another 31.25% stake in three years.
Before STO, Alibaba acquired minority stakes in three other large Chinese couriers - YTO Express Group Co Ltd, Best Inc and ZTO Express (Cayman) Inc.
Shanghai-based Yunda, which went public through a backdoor listing in 2016, is one of several couriers that work with Alibaba under Cainiao, the e-commerce firm's logistics division launched in 2013.
Cainiao provides software and shares data with warehouses, carriers and other logistics firms that help deliver packages to shoppers on Tmall and Taobao, Alibaba's largest e-commerce sites.
By Julie Zhu and Kane Wu