But he's heard the whispers. At 6-foot-3 and 234 pounds, he doesn't have the size to play tight end in the NFL. And he's not one of the athletic freaks who dominated the draft last year, like his former Badgers teammate Travis Beckum (third round, Giants) or Jared Cook (third round, Tennessee) or Shawn Nelson (fourth round, Buffalo).
So, Graham arrived here in Mobile, Ala., with plenty to prove. Is he big and strong enough to battle the big boys, and is he fast enough to make defenses pay for matching a linebacker against him?
"I want to prove that I'm a complete tight end playing against the best, that I can block, run routes and receive," Graham said Monday after the first Senior Bowl practice.
Graham was an all-Big Ten selection this past season (first team by media, second team by coaches) after catching 51 passes for 624 yards and seven touchdowns. Some scouts see Graham shifting to more of a fullback or H-back type of role, which would take advantage of his pass-catching skills but prevent him from having to in-line block against a 300-pound defensive end.
"I've always played tight end," Graham said. "I'll play wherever they put me. Whatever they draft me for, that's what I'll do. I'll find my role."
Tight ends have gone from something of a throwaway position to a big deal over the last decade, with eight of them hauling in more than 75 passes this season. And while pass-catching marvels like Antonio Gates and Tony Gonzalez will always be coveted, there's something to be said about a move-the-chains type of tight end. In the Super Bowl, the Colts boast Dallas Clark (100 catches, 10 touchdowns) while the Saints feature Jeremy Shockey and David Thomas (combined 83 catches). The conference losers had talented second-year pro Dustin Keller (12 catches, three touchdowns in playoffs) and Visanthe Shiancoe (11 touchdowns).
Don't mistake Graham for a plodder, though. He's plenty athletic, but he just doesn't have that eye-opening explosiveness. What he does have are sure hands, a knack for getting open and decent long-range speed.
He has garnered plenty of attention from scouts, and has met with the Packers, Bears and Vikings, "among others," he said.
"Hopefully, they like what they see," he said.
Bill Huber is publisher of Packer Report magazine and PackerReport.com and has written for Packer Report since 1997. E-mail him at email@example.com.