Thompson spent last season with the Bears, recording seven tackles on defense and eight on special teams in 10 games. Thompson, who was inactive for all 16 games as a rookie with Jacksonville in 2004, is 6 feet, 190 pounds.
He took part in Wednesday afternoon's practice.
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Wide receiver Kelly Campbell appeared to aggravate a leg injury while making a catch near the sidelines. Campbell was wearing a red jersey at practice, indicative of a player who is injured but can still work.
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Booker has a minor calf injury, while McKinney reportedly is undergoing tests to determine the extent of an upper-body injury.