The person spoke on the condition of anonymity because the deal has not been finalized. Several outlets reported late Thursday that Thomas was headed to Chicago.
The 37-year-old Thomas gives the Bulls a strong defender and rebounder in the frontcourt to go with Joakim Noah and Carlos Boozer.
Thomas has averaged 8.8 points and 7.0 rebounds for seven teams in his 15-year career, including a seven-season run with the New York Knicks.
He averaged only 3.0 points and 4.2 rebounds with Milwaukee last season, but was effective in the playoffs, contributing 7.9 rebounds as the Bucks pushed Atlanta to seven games.