League sources told ESPN and MLB.com on Tuesday that Bauer is headed to the Reds as part of a three-team trade that includes the San Diego Padres. The Indians are acquiring outfielders Yasiel Puig and Franmil Reyes and left-hander Logan Allen, while the Padres will add OF prospect Taylor Trammell.
The clubs haven't confirmed the deal.
Bauer, who made his first All-Star Game in 2018, has a 9-8 record with a 3.79 ERA and 185 strikeouts in 24 starts this season. The 28-year-old pitcher is making $13 million this season and isn't a free agent until after the 2020 campaign.
Earlier Tuesday, MLB informed Bauer that he would be fined, but not suspended, after angrily throwing a baseball from the mound over the center-field fence at Kauffman Stadium against the Kansas City Royals, according to the MLB Network.
In eight seasons with the Arizona Diamondbacks and Indians, Bauer is 68-55 with a 3.92 ERA and 1,111 strikeouts in 174 career starts.