In Seattle, Will Dissly has emerged as the team's top tight end. The second-year pro has 12 catches for 124 yards and three touchdowns through three games this campaign.
Vannett, a third-round pick in 2016, has recorded 48 catches for 462 yards and four touchdowns during his first four NFL seasons.
With Vannett leaving, the Seahawks are expected to sign fellow tight end Luke Willson, a source told NFL Network's Ian Rapoport. Willson played for Seattle from 2013-17, making two Super Bowl appearances and catching all 11 of his career touchdowns.