The newspaper quoted an unnamed source as saying that Graham is "generally considered unlikely to be back in Seattle."
Graham, 31, was playing on the final year of a four-year, $40 million contract. He signed that deal in 2014 with the New Orleans Saints, before being traded to the Seahawks.
Graham had his best year for the Seahawks this season, pulling in 57 catches for 520 yards and 10 touchdowns. It was the first time he had double-digit scores since 2014.
Seahawks defensive end Michael Bennett could also be released this off-season. He is still under contract through 2020. The 32-year-old defender recently told the News Tribune that he could see the franchise looking to go younger.
"I probably won't be back next year," Bennett told the News Tribune. "Just seems like it's a young man's game. I can see them going younger, with younger players. That's part of the game."
Seahawks quarterback Russell Wilson, who is close friends with Graham, spoke glowingly about the tight end in his post-game comments Sunday.
"Personally, I just hate losing and I know there are a lot of guys in the locker room that do, too," Wilson said. "It's disappointing, we put so much work in. I think about this off-season, I think about all the work that guys put in together, and all the straining, all the movies, all the early mornings and everything in the off-season. Then you come back together and you're looking forward to something great in the OTAs and all that. Then you go away for a little bit in the summer time, you come back for training camp, and a lot of blood sweat and tears go into training camp, and you do everything you can. Then, you begin the season with very, very high hopes and everything else, and you battle. Some of our great players went down, and everything else, and they were still great leaders. Then, you have guys step up into certain roles and play great.
"When I think about this season, I think about guys like Shaq Griffin, I think about him stepping in and making great plays. I think about Dion Jordan and I think about what he did to get back on a football field again, just to play again. I think about all the things he was fighting to do, to be able to play football again, and the great player that he was and that he came back to be this year. I think about the guys like Shead, and guys stepping up. I think about guys like Mike Davis, stepping into a role that he didn't know he was going to be in, but played great in.
"Getting guys like Duane Brown on our football team that were great leaders and great people and great professionals. I think about guys like Jimmy Graham and the plays that he's made all year and the exciting plays that he's made in the end zone. And Doug Baldwin making some great catches like tonight. I think about Paul Richardson's season and all the times this past offseason that we got to throw together and work together and train together. Tyler Lockett fighting back from injury, and all the things that he did. I think about Cliff Avril, the man that he is and the family that he has and the things that he's had to battle through the past few months. Guys like Kam Chancellor and people like that. Richard Sherman, who is one of the greatest football players that has ever stepped on a football field. So those are the things that I think about right now. I think about those guys."