The Bears were one of the teams to inquire about Johnson on Saturday on the opening day of the NFL's legal tampering period leading up the official start of free agency on Tuesday at 3 p.m. CT, according to a source familiar with the situation.
ESPN.com's Minnesota Vikings NFL Nation beat reporter Ben Goessling had reported that seven teams had contacted Johnson's representatives by Saturday evening, including the division rival Vikings.
The 6-foot-7, 270-pound Johnson recorded only 3.5 sacks last season to go along with 56 tackles, one interception and two forced fumbles.
However, Johnson, 27, had a career-high 11.5 sacks in 2012.
In five years with the Bengals, Johnson has 26.5 sacks, three interceptions and three forced fumbles.
The Bears are in dire need of help at defensive end. Veteran Julius Peppers' future with the Bears is cloudy at best considering the eight-time Pro Bowl pass-rusher is scheduled to count $18,183,333 million against the club's 2014 salary cap.
Further complicating matters is that former first-round draft choice Shea McClellin is moving to linebacker next season, and Corey Wootton is set to become an unrestricted free agent. Wootton is currently recovering from offseason hip surgery and not expected to return until the summer.
The Chicago Tribune reported on Saturday the Bears are believed to have expressed interest in free agent defensive end Michael Bennett, whose brother Martellus is the team’s starting tight end.
Addressing the defensive end position is clearly a priority for the Bears in the coming days.