The person spoke Tuesday on the condition of anonymity because a deal had not been announced.
The Chicago Tribune, citing sources, reported Teague will earn his slotted salary of $857,000 next season and is expected to make 120 percent of the slotted rate in the following years.
A Kentucky product, Teague was taken with the 29th pick and is expected to fill a backup role at point guard. The Bulls signed Kirk Hinrich and Nate Robinson in an effort to get by while Derrick Rose recovers from a major knee injury.
Teague averaged 10.0 points and 4.8 assists to help Kentucky win a national title in his lone season. Older brother Jeff plays for Atlanta.