This comes after the Falcons brought in free agent kickers Elliott Fry and Younghoe Koo for workouts on Monday.
Bryant, 44, began his NFL career with the Giants back in 2002. He had stints with the Cowboys, Colts, Dolphins and Buccaneers before eventually signing on with the Falcons in 2009.
The Falcons re-signed Bryant last year to a three-year, $10.5 million contract before releasing him during the offseason. Atlanta brought Bryant back at the start of the regular season.
In 2019, Bryant is 9 of 14 (64.3 percent) in field goal attempts to go along with 14 of 15 in extra point tries over the course of seven games.