The Browns acquired Beckham from the New York Giants in March for a first-round pick, third-round pick, and safety Jabrill Peppers in a stunning blockbuster trade.
"I don't see this relationship ending well," said Glazer.
Beckham is struggling to find chemistry with quarterback Baker Mayfield during his first year with the Browns, hauling in just 57 catches on 103 targets for 805 yards and two touchdowns.
The three-time Pro Bowl receiver gave a vague response Thursday when asked if he wants to stick with the Browns next season.
"No one knows what the future holds tomorrow," he said. "I couldn’t tell you what's going to happen."
"In the offseason, everything will figure itself out," he added. "I feel like I've been here before, answering questions about the next team when I'm on a team already. That's just something I'm going to tune out for right now. Catch me in the offseason, and we'll see what happens. I don't know God's plan."
The receiver later clarified his message on Twitter, responding to speculation that he's unhappy in Cleveland.
The Browns haven't lived up to the lofty expectations that followed Beckham to northeast Ohio, and they sit out of the playoffs at 5-7 entering Week 14.
Beckham is reportedly expected to undergo offseason surgery for a sports hernia that's contributed to his underwhelming play this year.
The 27-year-old is signed through 2023, but the Browns would only absorb a $2.75-million cap hit if they trade or release him this offseason, according to Spotrac.