Briggs, 34, just completed the final season of a three-year contract with the team.
Over 12 seasons in Chicago, he recorded 1,174 total tackles, 15 sacks and 16 interceptions.
Briggs played in at least 14 games in each of his first 10 seasons but injuries limited him to 17 combined games in 2013 and 2014.
According to the report, Briggs has yet to speak with new general manager Ryan Pace or coach John Fox, who replaced Phil Emery and Marc Trestman, respectively.
Earlier this month the Bears hired Vic Fangio as their defensive coordinator.
From the Chicago Tribune report:
"The closure I had there was a different GM, different coach," Briggs said. "My understanding there was this was my last year and I am moving on.
"New GM, new coach, we haven't had those kinds of talks yet. Obviously the door is open until we have that conversation and I know how they feel." [...]
"In Vic Fangio's defense, if he has a place for me, I'll play it," Briggs said.
Chicago went 5-11 and finished last in the NFC North last season.