Bauer went 12-8 with a 4.26 ERA last season when he made just less than $1.7 million.
Bauer, who turns 26 on Tuesday, was in the news during Cleveland's run to the World Series when he cut the pinky finger on his pitching hand while repairing a drone.
He was pushed back one game in the rotation but the finger hadn't healed and it started bleeding profusely, causing him to depart after just two outs in an American League Championship Series start against the Toronto Blue Jays.
Bauer was 0-2 with a 5.27 ERA in five postseason appearances (four starts, one relief). Both losses were in the World Series against the victorious Chicago Cubs.
He set career best for victories and innings (190) last season and struck out 168.
Bauer is 30-32 with a 4.42 ERA in part of five seasons with the Arizona Diamondbacks (2012) and the Indians.
Seven other unsigned Cleveland players are eligible for arbitration, including standout right-handed closer Cody Allen. Also eligible are right-handers Zach McAllister, Dan Otero, Danny Salazar and Bryan Shaw, plus outfielders Lonnie Chisenhall and Brandon Guyer.