The Hawks confirmed that Teague has signed a four-year, $32 million offer sheet with Milwaukee, where he would be reunited with ex-Atlanta coach Larry Drew.
The Hawks have three days to match the offer.
General manager Danny Ferry said the team is considering its decision with Teague.
“As we have consistently said, we value Jeff,” Ferry said. “We are in the process of putting together what we believe is a strong foundation for this team and will make the best decision moving forward for our organization.”
Teague, a four-year veteran and two-year starter, set career highs with his averages of 14.6 points and 7.2 assists last season.
Schröder, 19, has played professionally in Germany since 2009-10. He will participate in the Hawks’ Summer League
Schröder, selected No. 17 overall, was the second of two first-round picks for Atlanta. Lucas Nogueira, a 7-foot center from Brazil, was the No. 16 pick and remains unsigned.
The Hawks say Schröder asked his name be changed from the English spelling Schroeder, as it was at the draft.
Meanwhile, Hawks coach Mike Budenholzer completed his staff by naming Taylor Jenkins as an assistant. Jenkins most recently coached the Austin Toros of the NBA Development League.
Jenkins worked with Budenholzer, the former San Antonio assistant coach, last year when he served as an assistant on the Spurs’ summer league team.
Jenkins interned with the Spurs basketball operations department during the 2007-08 season.