Bauer's agent, Rachel Luba, announced the decision Wednesday on social media. However, Luba said Bauer remains open to a potential return to Cincinnati.
"Why wait for the QO to expire to state the obvious," Luba wrote on Twitter. "... Trevor Bauer has rejected the QO but not the Reds, [and] he looks forward to speaking [with] them [and] all other interested teams [through] free agency."
The 29-year-old Bauer posted a 5-4 record and a National League-leading 1.73 ERA across 11 starts this past season. He is a finalist for the 2020 NL CY Young Award.
Bauer, who was one of only six players in Major League Baseball to receive the qualifying offer, had a $17.5 million salary in 2020. Players have until Nov. 11 to decide whether to accept the qualifying offer.
If Bauer chooses to sign with another MLB team, the Reds will receive draft-pick compensation in the 2021 draft.
In nine seasons between the Arizona Diamondbacks, Cleveland Indians and Reds, Bauer holds a 75-64 record with a 3.90 ERA. The D-Backs drafted him with the No. 3 overall pick in 2011 but eventually traded him to Cleveland in a three-team deal in 2012. He spent seven seasons with the Indians before being shipped to the Reds in 2019.
Bauer is widely considered the top pitcher in this year's free-agent class.