Hill was barred from all team activities in April after audio surfaced of him discussing injuries sustained by his 3-year-old son. Hill also told his fiancee, Crystal Espinal, she "needs to be terrified of me too, [expletive]."
"I'm just here to man up to what I did," Hill told reporters Sunday. "On the audio, my bad language, I'm gonna man up to that. I don't want anybody talking to my little sister or my daughter or my mom like that."
The audio mentioned Hill punching his son in the chest. Hill said Sunday the comment "would probably refer to me teaching my son how to box."
The NFL announced earlier this month that Hill would not be suspended for violating the league's personal conduct policy. Hill will continue to be subject to conditions -- including clinical evaluation and therapeutic intervention -- set forth by the Johnson County, Kan., district court, Commissioner Roger Goodell and the Chiefs.
Hill is entering the final year of his rookie contract. He had 87 catches for 1,479 yards and 12 touchdowns last season.
Hill has made three Pro Bowls since entering the league in 2016. The former fifth-round pick has 223 catches for 3,255 yards and 25 touchdowns over the past three years. He has also scored four punt return touchdowns and returned a kickoff for a score in 2016.