Shares of the Seattle-based e-commerce giant at last check were off 0.3% to $3, 211.76.
The talks value Wondery at more than $300 million, The Wall Street Journal reported, citing people familiar with the matter. Wondery's last funding round, in June 2019, valued the company at $100 million.
Wondery's podcast shows include "Death of a Starlet," "Little Stories Everywhere" and "Jacked: Rise of the New Jack Sound."
The company is on track to increase revenue to more than $40 million this year, with about 75% of that coming from advertising and the rest from licensing to TV, subscription services like Audible and Stitcher Premium, and Wondery's own premium subscription service, which launched this summer.
The deal talks are ongoing and negotiations could still fall apart, the people said.
Closely held Wondery, Culver City, Calif., is the last large independent podcaster on the market, the Journal reported, and could present the final opportunity for a major tech or media giant to buy its way into the exploding field.
Wondery's investors include venture-capital firms such as Waverley Capital, Lerer Hippeau Ventures, Greycroft Partners and Advancit Capital.
Several other podcast and related companies have been the subject of deals by major players in the tech and media sectors.
Gimlet Media, a maker of narrative podcasts, was acquired by Spotify in 2019 for more than $200 million.
In late October iHeartMedia (IHRT) - Get Report agreed to acquire the podcast marketplace and tools provider Voxnest.
And In July, New York Times (NYT) - Get Report said it would acquire Serial Productions, maker of the hit podcast "Serial," in a deal that could be valued as much as $50 million depending on milestones and performance metrics, according to the Journal.