Prince Amukamara spent the morning having fun with his teammates. Every so often, he would look at the door to the locker room or a meeting room, flash a big smile and yell: "Jason!"

Everyone would turn around to see . . . no one.

"I think everyone is excited to finally see him back," said wide receiver Rueben Randle, a repeated victim of Amukamara's crying wolf. "Whenever he gets here, I think he'll get a lot of love from his teammates."

Jason Pierre-Paul did arrive in New Jersey on Monday for his first face-to-face meeting with the Giants since he injured his right hand in a fireworks mishap July 4.

After landing at Newark Liberty Airport, he traveled to the Hospital for Special Surgery in Manhattan, where he was examined by the team's medical staff before stopping by the Giants' facility in East Rutherford to meet briefly with members of the coaching staff and front office, including Tom Coughlin.

Amukamara said Pierre-Paul "instantly" will make the defense better. It's unlikely, however, that his return to the field will be that quick.

The Giants are getting their first chance to see the damage to his hand, which includes the amputation of his right index finger. That could take a day or more to digest. Then they must agree to a contract with him. The $14.8-million franchise tag is the starting point, with the team almost certain to ask for a reduction to that number based on how much -- and how well -- they project he can play this season.

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Some close to Pierre-Paul believe he is in shape to play -- the NFL Network reported that his representatives have been sending training videos to the Giants to demonstrate his readiness -- but that could be a case of hoping the Giants are ready to pay.

Still, there is a very slim chance he could be on the field Sunday against the Cowboys.

"I'm not saying anything," Coughlin said of Pierre-Paul's availability. "Maybe he comes in and he's in great shape and the doctors clear him right away. He practices two days and he goes and plays. I don't know. I'm not sure about anything, but I'm not going to rule that out, either."

Coughlin did say he believes Pierre-Paul will have some catching up to do, both in terms of learning the new defense and getting into football-level condition.

"That's like asking me how hard is it going to be for a Ferrari to get going," defensive end Robert Ayers Jr. said. "That's what he is. The guy is a well-oiled machine and a very smart guy. I can't tell you how long it'll take for him to get things going."

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Ayers said it is more important for Pierre-Paul to rejoin the team than actually play.

"To have him back is going to lift everyone's spirit," he said. "Every day he's on our mind worrying about him, thinking about him, wishing him well. To see him back and see his smile and his energy that he brings to this unit, it's going to really lift us up . . . How he plays and if he plays and when he plays, that's another thing. But just being around your brother, that's big."

It won't be a reunion for everyone.

"If I do see him, I'm going to say 'hi' finally," said rookie Owa Odighizuwa, who has never met the player who soon will become his defensive linemate.

Those who already have had the honor, though, are very much looking forward to his return.

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"If he comes today, we instantly become a better defense," Amukamara said. "I'm excited. I keep hearing the rumors and hearing that he's coming. I'm just anxious and anticipating his well-being."

That's the biggest issue.

"We need a healthy Jason Pierre-Paul, certainly," Coughlin said. "First of all is his health."