The Bears, however, run the risk of losing Fuller without receiving compensation. If they opt not match an offer sheet, they will get nothing in return.
Bears general manager Ryan Pace expressed interest in retaining Fuller at last week's NFL scouting combine.
"Obviously we like Kyle, and he had a good season, and we're happy with the way he's progressed," Pace told reporters.
The 26-year-old defensive back looked all but done with the Bears before the start of the 2017 season, then turned in arguably his best season, with 67 tackles, two interceptions and 22 pass breakups.
Chicago brought in multiple cornerbacks last spring, in essence to replace Fuller. The 2014 first-round draft pick missed the entire 2016 season following a routine knee scope, which caused the team to decline his fifth-year option.
Fuller started 46 games for the Bears over four seasons.