The move was first reported by the Chicago Tribune.
The Bears signed Davis to a one-year contract on Aug. 6 after receiver Devin Thomas announced his retirement.
In his eighth year, Davis played his first six seasons with the Bears starting in 15 games while serving primarily as a four-phase special-teams contributor. In 103 career games, Davis has caught 92 passes for 1,095 yards and five touchdowns, in addition to returning 72 kickoffs for 1,400 yards.
Davis signed as a free-agent with the Detroit Lions prior to the start of the 2011 season. He played 11 games for the Lions last season and admitted the difficulty of competing against his former Bears teammates.