Speaking to NFL Network's Andrew Siciliano and Aditi Kinkhabwala, via NFL.com's Jeremy Bergman, Landry was asked about not hearing from Tannehill since the Dolphins traded him to the Cleveland Browns in March.
"We didn't really have a good relationship anyway, so I'm not surprised," Landry responded.
Landry's comments about Tannehill come one week after he told Cleveland.com's Dan Labbe the Browns' quarterback situation is much better than what Miami had.
"The quarterback play is so important, which has got me that much more excited about Tyrod [Taylor] and [Baker Mayfield] and the way that they're throwing the ball out here, it makes me that much more excited," he said. "It's a lot better than what I had in Miami. I'm excited about that."
The Dolphins put the franchise tag on the 25-year-old in February before dealing him to Cleveland. The Browns gave him a five-year extension with $47 million guaranteed in April.
Landry played with the Dolphins from 2014 to 2017 and caught at least 84 passes each season. He led the NFL with 112 receptions in 2017 with Jay Cutler at quarterback; Tannehill missed the season after undergoing surgery in August to repair a torn ACL.