According to the report, Advent has beat rival bidders to be the likely buyer after the bakery chain has asked for a valuation of $800m to $1bn or more.
Earlier reports suggested that other private equity firms and industry players including Yum China, Jollibee Foods and Restaurant Brands International had shown preliminary interest in the company.
Founded in 1999 in Shanghai, Wagas now runs over 160 stores across 11 major cities in China.
Advent focuses on investments in chemicals, healthcare, consumer and retail in the Chinese market. Recent deals including buying into hard capsules producer GS Capsule last year and life sciences contract research company BioDuro in 2019.
On the consumer side, the firm had bought into Shanghai-based mattress producer King Koil China in 2016.
Fellow buyout houses had also been eyeing the enormous retail market in the country.
Primavera and Ant Financial-backed Yum China had reportedly rejected a $17.6bn buyout offer in 2018 from a consortium led by Chinese investment firm Hillhouse Capital Group.
Baring Private Equity Asia, KKR and Chinese sovereign wealth fund China Investment Corp were also part of the consortium.
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