Tait, a 10-year NFL veteran who spent the past five years with Chicago, is expected to retire. He was the 14th pick overall in the 1999 draft by the Kansas City Chiefs.
Tait played right tackle last season. The Bears are hoping to re-sign free agent tackle John St. Clair, who played on the left side last season, and move him to the right side vacated by Tait.
Chris Williams, the team's top pick a year ago whose rookie season was slowed by back problems, would then man the left side.
Earlier this offseason, the Bears added depth to their offensive line by agreeing to a four-year contract with free agent offensive lineman Frank Omiyale. Earlier this week, they released veteran lineman Terrence Metcalf.
On Thursday, the Bears also signed defensive back Marcus Hamilton to a one-year deal.