Salguero tweeted that Landry is available for the "right compensation" and that Miami is "not giving him away."
Landry later posted a cryptic message on his Instagram, alluding to a potential trade:
However, Josina Anderson of ESPN reported Landry was told Tuesday morning that the team would not be trading him.
The 24-year-old Landry is in the final year of his contract and can become an unrestricted free agent at the conclusion of the season.
He leads the Dolphins with 50 catches for 398 yards, and he is second on the team with three touchdown receptions.
The 2014 second-round pick out of LSU made the Pro Bowl in both 2015 and 2016, as he topped 1,100 receiving yards in each season.
In 2016, Landry finished with 94 grabs for 1,136 yards and four touchdowns.
The Dolphins are tied with the Jacksonville Jaguars for the final playoff spot in the AFC with a record of 4-3.
If they deal Landry, more of the receiving burden will fall on Kenny Stills and DeVante Parker, who has missed the past three games with an ankle injury.
Trading Landry could further damage a Dolphins passing attack that ranks 30th in the NFL with 176 yards per game.