Butler has already met with the Bears, but left Chicago without a contract agreement in place.
Butler, 30, is a former second-round pick of the Patriots back in 2009. He spent the first two years of his career in New England before he was waived and later claimed by the Panthers at the start of the 2011 season.
The Colts signed Butler as a free agent in September of 2012 and he has spent the past five years in Indianapolis.
In 2016, Butler appeared in 12 games and recorded 33 tackles, three interceptions, a forced fumble and six pass defenses. Pro Football Focus has him rated as the No. 20 cornerback out of 112 qualifying players.
We have him featured in our Top 50 Available Free Agents list.