Smith, who was the eighth overall pick in the 2018 NFL Draft, hasn't signed his rookie contract and is steering clear of the team until a deal is done, NFL Network Insider Ian Rapoport reported.
The 6-foot-1, 236-pound Smith helped lead Georgia to the national championship game last season, winning the Butkus Award as the top linebacker in college football.
Smith amassed 137 tackles, including 14 for loss, 6.5 sacks and two fumble recoveries during his stellar junior season. The 21-year-old clocked a 4.51 time in the 40-yard dash at the NFL Combine.
He is expected to step in immediately for the Bears and play alongside fellow linebacker Danny Trevathan.