"I don't see that relationship ending well for them after this year," Glazer said on Fox NFL Sunday.
Beckham was traded to the Browns last offseason after five years with the New York Giants but has struggled with 57 catches, 805 receiving yards and just two touchdowns in 12 games.
All three figures mark career lows. His previous worst of three touchdowns came in 2017 when he only played four games.
Meanwhile, Cleveland has struggled as a team with a 5-7 record after entering the year with lofty expectations.
Considering Beckham has played only one playoff game in his six years in the NFL, it's understandable for him to be frustrated.
"Odell Beckham Jr.'s exceptional talent has been wasted this season in what multiple sources describe as a dysfunctional Browns offense," Mary Kay Cabot of Cleveland.com reported Saturday.
The 27-year-old has four more years remaining on the contract he signed with the Giants, and it's unlikely the Browns will release him. That means for him to get a chance with a new team, it will have to come through another trade.