Cromartie will have the most pivotal defensive assignment on Sunday as he will likely shadow one of the best receivers in the game at Paul Brown Stadium. It's the first matchup between the two.
"It's a tough task. He's a great receiver for that team and he's one of the best receivers in the NFL right now," Cromartie said. "They want to try to get the ball to him."
Green, in his third year, is putting together another great season. He's caught 43 balls for 619 yards and five touchdowns, and ranks fourth in the NFL in receiving yards.
Jets coach Rex Ryan said he believes Green is probably the best receiver in the AFC, and Cromartie compared Green to Randy Moss and Calvin Johnson with his ability to be a deep-play threat, and how he gets after the ball. Green hauled in an 82-yard touchdown catch last week.
"He's an athletic guy that does a very good job of attacking the ball down the field. Can make all the catches and make the difficult catches look easy," Cromartie said. "It's a point of just being there and trying to make plays when the ball is in the air with him."
Cromartie, who has been shaky this season according to statistics, said there's no extra excitement in facing perhaps the best young receiver in the game. He approaches each assignment the same way, whether he's shadowing a future Hall of Famer or a rookie.
The Bengals line Green up in different positions, including the slot, and Cromartie said he can play all the different positions needed to follow Green on Sunday. Cromartie is your prototypical corner who sticks to outside receivers, and doesn't usually cover slot receivers.
The veteran has made it a point recently to be more physical with receivers, and Thurman said there was "no doubt" Cromartie did a better job of doing so last Sunday against New England. Being physical in coverage will be key to disrupting Green and getting him off his routes.
"[When] he plays to his height and his length, he's hard to deal with," Thurman said. "It's a matter of continual focus: 'Hey, you need to play like this, you need to play like this.' When he does that he's hard to throw at."
Cromartie said his height may give him a weapon other cornerbacks don't have when guarding Green, who stands at 6-foot-4.
"I think we're about the same height. That's the only difference it's going to be out there," Cromartie said. "Just not facing a 5-11, 6-foot DB. He's facing a 6-2, 6-2 1/2 DB. Just the matchup being two tall guys going out there and matching up against one another."
Just as Cromartie expects to have his hands full on Sunday, Green believes he's going to have just as tough of an assignment in trying to separate from the Jets' top cornerback.
"He's a great corner. Like I said, he's been around this league a long time," Green said. "Corners are going to get beat here and there but I think he’s one of the best in the league."