Hunt, who is in the final year of a two-year, $12 million deal he signed two years ago, has not participated in team drills the last two practices because of his desire for the extension.
The news of Hunt’s trade demand was first reported by Cleveland.com.
Hunt’s situation adds more drama for the Browns, who are waiting to see how long quarterback Deshaun Watson will be suspended for violating the NFL’s personal conduct policy.
The 27-year-old has been productive during his three seasons for Cleveland, but he missed nine games last season with calf and ankle injuries and finished with 386 yards and five touchdowns.
The Associated Press contributed to this report.