Hunt, who is in the final year of a two-year, $12 million deal, had missed team drills the past two practices but returned to them on Sunday.
The news of Hunt's trade demand was first reported by Cleveland.com.
Browns coach Kevin Stefanski declined comment Sunday when asked about Hunt's trade request.
"I'm not going to get into really anything that has to do with our players and conversations," he said.
Stefanski also said he "won't get into that" when asked whether Hunt would be fined for sitting out team drills.
Hunt's situation adds more turmoil for the Browns, who are waiting to see how long quarterback Deshaun Watson will be suspended for violating the NFL's personal conduct policy. Watson was suspended for six games by disciplinary officer Sue L. Robinson on Monday, but the NFL appealed the ruling Wednesday, seeking a tougher penalty.
Hunt, 27, 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, finishing third on the team in rushing behind Nick Chubb (1,259 yards) and D'Ernest Johnson (534). Hunt led the Browns with 11 touchdowns (six rushing, five receiving) in 2020.
Hunt, who led the NFL in rushing as a rookie with the Chiefs in 2017, when he had 1,327 yards, was released by Kansas City a year later after video surfaced of him shoving and kicking a woman. He signed with the Browns in 2019 and was suspended for the first eight games of that season for violating the personal conduct policy.
ESPN's Jake Trotter and The Associated Press contributed to this report.