Quarterback Russell Wilson is reportedly "recruiting him hard."
Pryor is coming off a disappointing season with Washington, in which he had just 20 catches for 240 yards and one touchdown in nine games.
The converted quarterback had a huge season with the Cleveland Browns in 2016, when he grabbed 77 catches for 1,007 yards, but he only signed a one-year deal in the offseason with Washington worth $6 million.
This ended up being a mistake, as Pryor struggled to get on the same page with Kirk Cousins before finishing the season on injured reserve with an ankle injury.
Still, the 28-year-old has a market for his services thanks to his size at 6'6" and athleticism, along with past success with Cleveland. Mike Silver of Sports Illustrated previously reported the Rams, Browns and 49ers were all trying to sign the receiver.
Meanwhile, Seattle needs to add pass-catchers after losing Jimmy Graham and Paul Richarson to free agency this offseason. The team already added former Cardinals receiver Jaron Brown, per ESPN, but he has never caught more than 31 passes in a season.
Pryor could make an immediate impact for Seattle in Graham's role. Graham scored 10 touchdowns last season.
Although there would certainly be risk in adding a player who struggled so much in 2017, his upside makes Wilson's heavy recruitment understandable.