The team announced Monday it placed a second-round tender on the running back.
Hunt is a restricted free agent. He could sign a contract with another club, which would send a second-round pick to Cleveland in return.
Earlier this offseason, Hunt had his latest off-field issue after marijuana was found in his car during a traffic stop. Police later declined to charge Hunt with possession of marijuana.
Hunt served an eight-game suspension for domestic violence to open the 2019 season. In eight games in Cleveland last year, he carried the ball 43 times for 179 yards and two scores, and added 37 receptions for 285 yards and one TD.