The former linebacker, who spent his entire 12-year career with the team, earned 10 Pro Bowl nominations.
Singletary is currently the linebackers coach for the Minnesota Vikings.
Singletary, 54, spent his entire 12-year NFL career with the Chicago Bears from 1981-92. He was a 10-time Pro Bowler and a seven-time First-Team All-Pro.
His only head coaching experience in the NFL came over three seasons with the 49ers between 2008 and 2010. In 2008, he replaced Mike Nolan mid-season and led the team to a 5-4 record. His only full season with the 49ers was 2009 when he led them to an 8-8 record.
After starting the 2010 campaign 5-10, he was fired mid-season.
Singletary has served under head coaches Nolan, Brian Billick and Leslie Frazier.
Singletary is one of many candidates the Bears are considering. The team has already interviewed, or will interview, Seattle Seahawks offensive coordinator Darrell Bevell, Green Bay offensive coordinator Tom Clements, Indianapolis Colts offensive coordinator Bruce Arians and Houston offensive coordinator Rick Dennison, among others.