The deal could launch in Hong Kong in the first half of next year, the Thomson Reuters publication reported, citing people close to the process.
Good Doctor's plans to list come as Hong Kong has hosted a series of "hot" tech stocks whose first-day gains have been among the best in the world this year, boosting the city's reputation for tech listings.
Users can consult doctors for diagnosis on the platform, which also provides online appointment booking. It does not currently provide prescriptions.
In 2016, Good Doctor raised $500 million in an initial funding round, valuing it at $3 billion.
Ping An declined to comment.
(Reporting by Fiona Lau and Julie Zhu, writing by Jennifer Hughes; Editing by Himani Sarkar)