"No question," Hunt told reporters Monday. "We can do something special here. I want to get that Super Bowl feeling and I believe we can do it here in my hometown.
"That would be bigger than anything, for me. That would bring a championship to Cleveland, especially -- I have been a fan my whole life. I have been with Cleveland my whole life."
He appeared in 11 games for the Chiefs in 2018 before he was released after he was shown shoving and kicking a woman in a video released by TMZ. The NFL then suspended Hunt for eight games before he joined the Browns.
Hunt is now a backup to Browns starter Nick Chubb but still is expected to see a lot of snaps out of the backfield and has met virtually with the team's wide receivers this off-season.
Hunt said he has "moved on" from his time in Kansas City. He also said his former teammates "deserved" to win the Super Bowl in February.
The 5-foot-11, 216-pound playmaker had 464 yards from scrimmage and three touchdowns in eight games last season. The Browns were a preseason favorite to make the playoffs but finished their 2019 campaign with a 6-10 record.
Hunt said he was "slowed" down last season after had had sports hernia surgery.
"That was definitely something that slowed me down last year in training camp and coming back, because I was rehabbing through my whole situation," Hunt said.
"Honestly, I feel like having a full season to train healthy and push myself and prepare myself for this upcoming season. And my body, I feel like it can be great. I am feeling good. I want to see how I feel fully healthy."
NFL team facilities have yet to open to all players due to coronavirus pandemic safety precautions.
Teams have met virtually throughout the off-season since major sports leagues were suspended in the United States in mid-March. The NFL Players Association said Saturday that players should stop "practicing together" in private workouts until the tentative date for training camps in late July.
The Browns have had one winning season since 2002. Cleveland has won just 21 percent of their games since the start of the 2015 season.