The firm, an avid investor in China's tech startups, is targeting $4 billion for its fourth dollar fund, with a hard cap at $5 billion, said the people, who declined to be identified as information related to the fundraising is confidential.
It is aiming to reach a first close within the next two months, one of the people said.
Primavera, which has offices in Beijing and Hong Kong, did not immediately respond to a request for comment.
The fundraising comes amid heightened regulatory scrutiny of China's technology giants which has clouded their near-term outlook.
Tighter grip on the sector came after authorities' November suspension of Ant's Shanghai and Hong Kong dual listing, which delayed the hefty returns early investors could have expected from the world's biggest initial public offering.
The financial technology giant was set to raise $37 billion at a valuation of $315 billion. It has since agreed a restructuring plan with regulators, Reuters reported in February.
Primavera invested in Ant's 2016 and 2018 fundraising, during which the company's valuation leapt from $60 billion to $150 billion. The private equity firm's founder and chairman, Fred Hu, serves as an independent non-executive director on Ant's board.
Another Ant investor, Boyu Capital, is also targeting $6 billion for its new dollar fund, Reuters reported last month.
In February, Taiwan's CTBC Financial Holding Co Ltd said it would invest no more than $20 million in Primavera's fourth dollar fund via unit Taiwan Life, without mentioning the total amount the fund was seeking.
Primavera has led investments in over 50 companies across tech, consumer, financial services, healthcare and education sectors, its website showed. It teamed up with Ant in the $460 million spin-off of Yum China Holdings Inc in 2016 and also invested in short video streaming giant Bytedance and online wealth platform Lufax Holding Ltd.
The firm more recently invested in community grocery shopping app Xingsheng Youxuan and job search site Zhaopin.com, and raised $414 million for a special-purpose acquisition company.
It closed its third dollar fund in November 2019 at $3.4 billion. Investors included CTBC and the Pennsylvania State Employees' Retirement System, public disclosure showed.
(Reporting by Kane Wu in Hong Kong; Additional reporting by Yan Zhang in Beijing; Editing by Sumeet Chatterjee and Christopher Cushing)
By Kane Wu