Landry, who was traded to the Browns this offseason and signed a five-year, $75.5 million extension with the team, told the website that he talks with Beckham frequently and the New York Giants wide receiver "definitely" would be open to playing in Cleveland.
"If things like that are able to happen and the team can make it happen, then why not?" Landry told cleveland.com. "He definitely would be [up for it]. He would be."
Asked if Beckham told him that, Landry said with a smile, "We've had talks, but at the end of the day, I want him to be happy. I want him to get what he deserves and you can't put nothing on that regardless of where it's at."
Landry made his comments in the wake of Cleveland trading wide receiver Corey Coleman to the Buffalo Bills on Sunday. There has been no indication the Giants are looking to trade Beckham.
Beckham, who is entering the last season of his rookie deal, has been seeking a contract extension from the Giants. Beckham's agent, Zeke Sandhu, left the New York area on Monday with no deal in place after face-to-face meetings with the team last week, a source told ESPN's Josina Anderson.
The Giants are valuing Beckham at a total average annual value -- when including his 2018 salary of $8.5 million -- below Chiefs receiver Sammy Watkins, who has an average annual value of $16 million in his current deal, a source told Anderson.
On Saturday, Beckham said at a news conference that his contract situation is trending in the right direction and he was "optimistic" a deal could be worked out.
Coleman was listed as a starter on the Browns' initial depth chart. Rookie Antonio Callaway and third-year receiver Rashard Higgins are expected to get the first opportunities to fill that spot now. The Browns also have Josh Gordon, who has missed camp while seeking treatment for his mental health and anxiety as part of his recovery from substance-abuse problems.
The Browns also have said they would consider veteran wide receiver Dez Bryant, but a source tells ESPN's Anderson there is an impression that Bryant is not seriously interested in playing for the Browns. While there are people with the team who would consider signing Bryant if he were engaged in playing in Cleveland, Bryant's "name has not come up in while."
Landry and Beckham were teammates with LSU from 2011-13 and both have starred in the NFL since being drafted. Landry has 400 receptions, 4,038 yards and 22 touchdowns in his first four seasons, all with the Miami Dolphins; Beckham has 313 catches, 4,424 yards and 38 touchdowns.
OBJ, Giants motivated to get deal done before season
Adam Schefter reports that both Odell Beckham Jr. and the Giants are pushing to get a long-term deal done.