The Atlanta Hawks have three days to match.
Talks between the Hawks and Teague have not gone well the past two weeks. New Milwaukee coach Larry Drew, who coached Teague for the past three seasons in Atlanta, helped recruit him to the Bucks, sources told ESPN.com.
The decision to go after Teague, plus a separate deal in which the Bucks have agreed to acquire point guard Luke Ridnour from the Minnesota Timberwolves, indicates they plan to move on from Jennings, their own restricted free-agent point guard.
Yahoo! Sports earlier reported Teague's intentions to sign the Bucks' offer sheet.
Faced with a decision about Teague, the Hawks signed point guard Dennis Schroder, a first-round draft pick from Germany.
General manager Danny Ferry says the team "will make the best decision moving forward for our organization."
"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 is included in a group of point guards from the 2009 draft who have risen to prominence during the past several seasons, including Stephen Curry, Ty Lawson, Jrue Holiday and Jennings. He had his best season in 2012-13, averaging 14.6 points and 7.2 assists in 80 games for the Hawks.
The 19-year-old Schroder has played professionally in Germany since 2009-10. The Hawks say Schroder asked his name be changed from the English spelling "Schroeder," as it was announced at the draft.
Information from ESPN The Magazine's Chris Broussard and The Associated Press was used in this report.