Ogbah didn't report for the start of the Browns' offseason program Monday in anticipation of being traded.
"Ogbah didn't show, and I'd rather talk about the guys that are here," Browns coach Freddie Kitchens said. I'm sure he's got his reasons. I don't know."
Ogbah, 25, was drafted in the second round (32nd overall) of the 2016 draft and has 12.5 sacks in three seasons with the team. He started all 40 games he played for the Browns.
In 14 games last season, he had three sacks and 40 tackles.
Browns general manager John Dorsey was the Chiefs' GM in 2016 when the team drafted Murray in the fourth round (106th overall). Murray appeared in 15 games last season, making nine starts; he had an interception, two passes defended and 55 tackles. He has appeared in 45 games for the Chiefs in three seasons, making 11 starts.
The Browns had waived safety Derrick Kindred earlier Monday.
Kindred, 25, had 33 solo tackles, an interception and a forced fumble in 16 games for the Browns last season. Drafted in the fourth round in 2016 (129th overall), he appeared in 42 games with the Browns, including 17 starts.
ESPN's Adam Teicher and Pat McManamon contributed to this report.