"Obviously, there are a lot of things off the field that he has to take care of," Nagy said Monday.
Nagy added he believes in "second chances but not third chances."
The Bears head coach has a familiarity with Hunt because he was the Kansas City Chiefs' offensive coordinator during the 2017 season. Hunt rushed for 1,327 yards and eight touchdowns as a rookie during that campaign.
The Chiefs released Hunt in November after video of him kicking and shoving a woman in a Cleveland hotel in February was published by TMZ. Hunt had started the first 11 games of the season before the suspension.
"It was just a long night," Hunt told ESPN's Lisa Salters. "To be exact, it don't really matter what happened. I was in the wrong. I could have took responsibility and made the right decision to find a way to de-escalate the situation."
Hunt admitted he lied to the Chiefs about what happened during their initial investigation into the incident. He was never charged with a crime.
"I've worked for this my whole entire life," Hunt said when asked if he hoped to play in the NFL again. "I gave everything and sacrificed so much for this. ... I'll do whatever I can to help win.
"That's not me. That's not the person I am. It's out there. It happened. I'm very embarrassed about it. I'm ashamed of myself."
The Bears already have Jordan Howard and Tarik Cohen on their roster, so it's unclear whether there's a football need for Hunt. Any team that signs Hunt likely will have to deal with a deluge of criticism, and some organizations may decline to avoid the backlash.
A team like Chicago, with a coach who knows Hunt personally, is probably his best chance at returning to the NFL. It just does not seem like a likely proposition for a team that is already set at the position and will go into 2019 as a Super Bowl contender.