Then the 12-year veteran and first-year Houston Texan let out a hearty chuckle.
''Teach him what?'' he bellowed. ''What am I going to teach J.J.?''
The big nose tackle has joined Watt, last year's Defensive Player of the Year, in Houston after spending the first 11 years of his career with the New England Patriots. While he isn't expecting to serve as a teacher to Watt, he thinks he could learn a thing or two from the 26-year old.
''He's a prime example of what the NFL is looking for when they talk about guys that know how to play this game and be a professional and be a human being,'' Wilfork said. ''He's a perfect person, so that's what I'm going to learn from him. We're going to compete every day.''
When asked what lesson he could learn from Wilfork, Watt joked about the 325-pounder's notorious love of food.
''I'm sure he can teach me how to barbecue, that's for sure,'' Watt deadpanned.
Watt and Wilfork have already developed a close relationship and are often seen talking and playing around together before and during practice. Watt said he sees Wilfork, who won two Super Bowl titles with the Patriots, as an older brother. Though Watt is one of the faces of the NFL and most likable guys in the league, the 33-year-old Wilfork sometimes grows tired of his antics.
''(Sunday) he told me: `Why are you messing around all the time, man?' I felt, at that moment, like the little brother that's like: `Hey, you want to play? Come on, let's go outside and play,''' Watt said. ''He had had enough of it. He was like: `I just want to work.'''
But Watt certainly gained some good will with Wilfork on Saturday when he took a minute to meet and take pictures with Wilfork's daughter Destiny.
''She said the only reason she was going to move here is if she got a chance to meet him,'' Wilfork said. ''I said: `OK' ... and I made that promise some months back. It finally paid off for me ... so I'm the best dad in the world right now.''
It's clear that Wilfork is fitting in nicely with his new team. But he's careful to let his teammates come to him and not try to push himself on them as they get to know him.
''This is my 12th year in the league, but I'm new here,'' Wilfork said. ''Just get a chance to let guys understand how I am, who I am, and what I'm here for. I'm all ears and I'm a sponge. You can sit and talk to me about anything in the locker room. They know that.''
Wilfork, a five-time Pro Bowler, joins a defense in Houston that not only has Watt, but also features last year's top overall pick Jadeveon Clowney. The outside linebacker is recovering from microfracture surgery, but is expected to return to practice on Aug. 17.
Watt has enjoyed watching Wilfork work so far and is looking forward to what he can bring to this team which is trying to return to the postseason after a two-year absence.
''For a big guy, Vince moves so well. He's so fluid,'' Watt said. ''He's so effective with what he does. You look at a guy his size and you would think there is no way he can do what he does but he's incredible and he works extremely hard at it.''
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