Landry reportedly lobbied his new team, the Cleveland Browns, to pursue Beckham when the Giants were listening to trade offers on the three-time Pro Bowl selection.
"Well you know what? I think that period is over and, you know, he's going to be a Giant for another year," Landry said, per the Cleveland Plain Dealer. "Outside of that, I'm just so focused on this team, I'm so focused on what we've got going with the guys we have now and the guys we'll add in a couple weeks."
Beckham hasn't spoken publicly on the matter, but he did show up with his New York teammates for the start of offseason workouts last week.
Attending voluntary workouts was a show of good faith for Beckham, who is seeking a long-term contract that will make him one of the NFL's highest-paid players. He is set to be paid $8.46 million this season.
Landry, a second-round draft pick, just signed a five-year extension worth $75.5 million that likely will serve as a baseline for Beckham's next contract. The Miami Dolphins placed the franchise tag on Landry before trading him to the Browns.
Beckham had his 2017 season cut short by the broken ankle sustained in October. Without him, the Giants slumped to a 3-13 record, and the offense finished 31st in the NFL in scoring at 15.4 points per game.
Beckham has 313 catches for 4,424 yards with 38 touchdowns in four seasons with the Giants. He was named the 2014 Offensive Rookie of the Year.