Assuming Martellus Bennett retires like he said he would and Dwayne Allen doesn't come back, Graham would be a massive upgrade to the tight end position. He would provide that Bennett-like insurance if Rob Gronkowski either retires or misses time next season, the latter more likely than the former.
Graham would add another big offensive weapon for Tom Brady and would give the Patriots the ability to run two tight end sets, which is something they love to do.
He has been pretty durable throughout his career as well, only missing six games since being drafted by New Orleans in 2010.
Of course, that's all well and good, but there are some caveats to this. The first is that Graham is not much of a blocker. If you're playing tight end in New England, you're going to have to block. Gronk does it, Bennett did it, Allen did it and so on.
Additionally, and probably more importantly, Graham is coming off a season in which he made $7.6 million with the Seahawks. If the Patriots were to ever consider signing him, he'd have to take a pretty big discount. I have no idea what the Patriots would offer him, but my guess is it'd be somewhere between $4 million and $5 million.
Given that Allen is supposed to make around that much next year and isn't nearly as productive offensively, I could see the Patriots cutting Allen and using the money to go after Graham. But I don't know how likely all of this is.
They'd be better suited investing money in their defense after it got carved up for four quarters in Super Bowl LII against the Eagles.