ESPN Giants reporter Dan Graziano provides an update on DE Jason Pierre-Paul's condition and the likelihood that he will play against the Buccaneers. (1:51)

EAST RUTHERFORD, N.J. -- The New York Giants are accelerating Jason Pierre-Paul's practice schedule this week in an effort to see whether he can be ready to play Sunday against the Buccaneers in Tampa, Florida. There's no guarantee he can or will be ready, but they definitely are leaving open the possibility that their injured defensive end could make his season debut this week.

"He's going to practice," Giants coach Tom Coughlin said Wednesday morning. "He'll practice today, he'll practice tomorrow, he'll get a good number of reps, and we'll take it from there."

Pierre-Paul returned to Giants practice last week for the first time since December, as he'd sat out the offseason program because of dissatisfaction over his contract situation and missed training camp and the first seven weeks of the season following a July 4 fireworks accident that severely damaged his right hand.

Asked if he thinks he'll play Sunday, Pierre-Paul said, "It depends. Maybe. It's up to the medical staff. They're taking me slowly. I want to play, absolutely, but as of now, they're taking it slowly. Coming off any injury, you've just got to go out there and get to the point where you're confident."

Pierre-Paul has impressed the team staff with the level of his conditioning, especially given how limited his physical workload must have been following the accident, and the staff has held extra padded practice sessions with just him twice in the past five days. Wednesday, Pierre-Paul was scheduled to work with the defense and the scout team, as the Giants want to try to get him up to speed quickly in a Steve Spagnuolo defense he hasn't yet learned.

During the portion of the practice that was open to the media, Pierre-Paul and the rest of the defensive linemen worked on a faraway field. It appeared he was going through all of the individual drills, as he did last Thursday, and that he was working with some kind of glove and/or pad on his right hand.

"Of course I have to change my stance. I'm right-handed," he said, "but it's something I've got to adjust to, and I think I'm doing a great job at it so far. I can play both sides [of the defensive line]. Nothing's changed."

Said Coughlin: "He's in outstanding physical condition. We knew that. We had him in pads on Saturday morning. We had him in pads on Monday. So we're feeling good about accelerating him along."

The Giants have a league-low nine sacks on the season, and they need help pressuring the passer. But Coughlin was blunt when asked whether the team's needs on defense would factor into the decision to play Pierre-Paul this week.

"No," Coughlin said. "It has to do with him and whether he's ready or not. If he's ready, we'll play him. If he's not ready, then we'll take more time."

The Giants have until 4 p.m. ET on Saturday to activate Pierre-Paul from the commissioner's exempt list if he's to be eligible to play Sunday. They would have to take someone off of the 53-man roster in order to add him.

The active roster bonus portion of his contract incentives don't begin until Week 10, but there's nothing in the contract that prohibits him from playing earlier than that.

"I know for a fact that I'm still the same JPP. If I couldn't do it, I wouldn't be here right now," he said.