The 6-foot-7, 265-pound tight end is among the most difficult matchups in the NFL.
"He's a unique cat," Jets coach Rex Ryan said Thursday. "He's got the speed of a receiver, the size of an offensive tackle. So it's a huge challenge."
Last season, his third in the NFL, Graham was tied for 13th in the league with 85 receptions, for 982 yards and nine touchdowns. The year before he was even better -- 99 receptions, 1,310 yards, 11 touchdowns.
The Patriots put top cornerback Aqib Talib on Jimmy Graham and held him without a catch.
In seven games this season, he already has 40 receptions for 630 yards and eight touchdowns -- putting him on pace to finish with 91 for 1,440 and 18.
Graham is playing through a foot injury -- he only played 18 snaps in the Saints' victory over the Buffalo Bills last Sunday. But he still made a big impact -- targeted three times, catching three balls, two of them for scores.
He's been limited in practice the past two days, but you can bet he'll be on the field Sunday at MetLife Stadium.
The question is, how will the Jets try to stop him? More specifically, who will they turn to?
Two weeks ago, the Jets faced a similar challenge in New England Patriots tight end Rob Gronkowski. Gronkowski did have eight catches for 114 yards in the game, but he was targeted 17 times.
Safety Antonio Allen was the man primarily responsible for guarding Gronk. "He did a good job," Ryan said. "From a body type, he's long and all that. So I think he did a good job."
But Graham -- listed as an inch taller than Gronkowski, and the same weight -- is even faster, multiple Jets players said Thursday.
Two weeks ago, when the Saints played the Patriots, the Pats put star cornerback Aqib Talib on Graham, as opposed to a safety or linebacker.
The result? Graham was held without a single catch for the first time in 46 games, since the middle of his rookie year.
So, would Ryan think about putting his No. 1 cornerback, Antonio Cromartie, on Graham this coming Sunday?
"It's a thought," Ryan said wryly, when asked the question Thursday.
Cromartie, like Talib, is a big cornerback -- 6-foot-2, 210 pounds. He hasn't had a good season thus far, but Ryan expressed confidence that Cromartie could do the job if asked.
"I think from a size (standpoint) and skill-wise, yeah I think he could handle him," Ryan said.
Cromartie did not speak with reporters Thursday. But linebacker Calvin Pace did.
"It's crazy, because Graham basically is a wide receiver, he just happens to be 6-7. It's a tough matchup, whoever you put on him. I don't want to guard him," Pace said, laughing.
"You put a safety on him, they've got a height advantage. It’s tough," Pace continued. "They do a good job of getting him in space so it's gonna be a person that's gotta get hands on him and just know where he is."
Cromartie will probably be that person Sunday, at least some of the time. Yes, Drew Brees has other weapons at his disposal -- wide receiver Marques Colston has 27 receptions for 342 yards, and fellow wideout Kenny Stills has 13 for 327, averaging 25.2 yards per catch. Plus don't forget about running backs Darren Sproles and Pierre Thomas.
But Graham is the man that must be stopped, or at least slowed down. If that means putting your best cornerback on him, so be it.