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Coughlin says he first heard about the incident Sunday afternoon July 5, one day after the accident occurred, and texted Pierre-Paul, "How can I help you?"
Three and-a-half weeks later, Pierre-Paul still hasn't responded, he told Vrentas.
"I want to help. I want to be there for him," Coughlin said. "But he's decided that he doesn't want our help. He thinks that something will come of it. But, all I care about, all any of us care about, the whole organization, is the well-being of the kid."
Pierre-Paul initially injured his hand July 4 in a fireworks-related accident. In addition to having to get his right index finger amputated, he also suffered a fractured thumb. Despite the severity of Pierre-Paul's injuries, they aren't believed to be career-threatening and he is expected to play at some point this season.
Two Giants officials - team trainer Ronnie Barnes and special assistant Jessie Armstead - attempted to meet with Pierre-Paul while he was in the hospital. The former first round pick, however, refused to see them. This still irks Coughlin, and has led the Giants head coach to believe Pierre-Paul and his camp may be attempting to hide something from the team.
"I don't know what he thought he was going to accomplish by not allowing them to be there to assist, to help, whatever needed to be done," Coughlin said. "I thought that was a really poor move by them. By his people. I don't know what they think they are hiding. It only makes us, me personally, think the worst."
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Giants owner John Mara described the fact that the team has yet to establish any communication and meet with Pierre-Paul as "very disappointing" when speaking with New York Post's Steve Serby and Paul Schwartz, and questioned the advice Pierre-Paul is getting from his inner circle.
"I don't think JPP is receiving very good advice right now," Mara said. "He has told people that he's fine and he's going to be ready to play, but until we see the hand, we're just not sure."
The Giants open training camp this Friday. Pierre-Paul, who technically is still not under contract with the team as a result of his refusal to sign his franchise tag, is not expected to attend. He reportedly won't sign his $14.8 million tender until he knows he can pass the team's physical, and be medically cleared to play, according to ESPN's Ed Werder.
If Pierre-Paul were to sign the one-year contract, and then fail his physical, the Giants would have the option to put him on the non-football injury list - forcing the defensive end to sit out at least the first six games of the season. Teams can elect not to pay players who are on the non-football injury list.