The 28-year-old Bauers hit .202 with 12 homers and 30 RBIs in 84 games and 272 plate appearances this year for the Yankees. He was called up April 29 when Aaron Judge strained a hip and got extensive playing time because of injuries to other New York regulars.
"That was a guy that we had targeted as a left-handed bat with power," Arnold said. "I think he had 23 home runs between Triple-A and the big leagues last year. He's athletic and he's really developed I think over the last 12 to 18 months, and he's changed some things in his swing that we're excited about."
Bauers is eligible for salary arbitration and likely to get a salary of $1.5 million to $1.75 million.
Avina, 20, hit .233 with 14 homers, 50 RBIs and 10 steals in 99 games this year for Class A Carolina. He was a 14th-round draft pick by the Brewers in 2021.
Sánchez, 19, batted .297 with 7 doubles, 4 triples and no homers in 33 games with the Dominican Summer League Brewers this year.
The decision to non-tender Tellez leaves Milwaukee with a hole at first base since Carlos Santana, who came to Milwaukee at the trade deadline, is now a free agent. Bauers could help in that regard.
The Associated Press contributed to this report.