"I don't know, only time can tell," Pierre-Paul said about playing in Week 1. "It's all on me to recover."
"That's everybody's goal who is hurt," he added of playing in the opener. "I don't know. I can't promise nothing. I can't say I will be back for the season opener."
Pierre-Paul was placed on the physically unable to perform list to start camp as expected. He did some light running on the side on Friday while his teammates went through a conditioning test.
The Pro Bowl defensive end, who is entering his fourth season, underwent back surgery on June 4 after he still felt pain in his back. The initial timetable for recovery has the defensive end potentially being ready to play in the opener against the Cowboys.
Pierre-Paul has a history of back issues but he said he first experienced the pain that led to his surgery about two years ago. The defensive end initially thought he could strengthen his core this offseason and ease the pain that way but when the pain returned in minicamp, he opted for surgery.
"The whole discomfort is gone," Pierre-Paul said. "When I sit down I don't have that pain any more. When I am standing up I don't have that pain. I can stand up straight. Basically everything is gone. That's a good thing. I am doing pretty good."
"I am happy I did the surgery," he later added. "Now there is nothing holding me back when I do get back."
Pierre-Paul said the pain had an impact on him last season when he saw his sacks dip from 16½ in 2011 to 6½ last year.
"A lot, it did," Pierre-Paul said how much the back pain held him back. "I can't give you a percentage because I don't know. It took a while to figure it out. At the end of the day, it was pain. As a defensive lineman, when you get in your stance, that hurts, you know what I mean, for the pain I had, that hurts. I didn't complain, I just dealt with it and played."
The Giants will take things slowly with their franchise defensive end to make sure he will be completely healthy for the upcoming season.
"I feel like I am at 75 percent," Pierre-Paul said. "I have been doing everything they asked me to. ... The doctors said I am doing pretty good there."
"I am feeling great now, I don't have no pain bothering me," he added. "A back [surgery] is a really, really horrible thing to have, back surgery period and you don't want to rush back. I'm not concentrating on the first game, the second game, the third game, fourth game, fifth game, sixth game. I'm just trying to come back when I feel like I'm ready to come back."