The ankle sprain he incurred last week in Jacksonville has already rendered him questionable and a game-time decision.
Instead, he said he plans to lobby the coaching staff to allow him to resume his starting running back duties, not because the Giants' season has any tangible meaning left, but because there are lessons to teach. To Jennings, finishing a season the right way is important, even one so devoid of hope as the current 3-9 debacle.
''We're still playing for so much,'' said Jennings, who took part in limited practice with his right ankle taped after sitting out the first two days. ''Everybody's playing for so much. Critiquing ourselves, getting better, creating building blocks, showing the younger guys how to finish.
''I always say nobody's forcing me to do this. I could walk right out of here, get in my car and go home. But I love this sport. I love this game.''
Jennings, the Giants' rushing leader with 598 yards and four touchdowns on 154 carries, owns a 3.9-yard average. That represents a full yard more than the 2.9 his backup Andre Williams has in 134 carries, including during five starting assignments while Jennings recovered from a midseason MCL strain.
The Giants rank 22nd in the league in rushing offense.
Between that and his injuries, 2014 has not been the kind of season the 6-foot-1, 234-pound Jennings expected. The former Jaguar and Raider signed a four-year, $10 million free agent deal this offseason.
But he said he has a chance to finish strong, providing the medical staff clears him.
''It matters how you finish,'' Jennings said. ''It matters because it sets a precedent for next year.
''We knew last week we weren't going into the playoffs. We're playing for pride, playing for the man beside you, playing because it's a privilege. This is our resume.''
The act of finishing has not been one of the Giants' strong points this year. In fact, the last four games of November saw fourth-quarter collapses that stretched a losing streak to seven games and put Tom Coughlin squarely on the coaching hot seat.
All Jennings can do now is improve his statistics and help his rookie backup, Williams, become a better player.
''Me and `Shad talk every day and we watch the film and he shares his wisdom with me,'' said Williams. ''That's the goal from the beginning, to finish, because that's the point. I certainly believe in that. I feel like, even though the record doesn't show it, I grew from the season and learned things about the game.''
Williams might have another chance to grow. If Jennings can't make it, Williams will start and Tulane rookie Orleans Darkwa, picked up from the Dolphins' practice squad Nov. 12, will become the primary backup. Darkwa could come in for third-down pass blocking.
''He's doing well. He's had a full week of practice in that role,'' Coughlin said.
Regardless if it is Jennings, Williams or Darkwa running the ball, Jennings wants to see an end to the current cycle. He'd like to be part of some improvement, pain or not.
''It matters how you finish,'' Jennings said. ''Andre and all the other running backs, just teach them how to finish. We watch the film, there's a lot of self-inflicted wounds. So my mindset is to be able to change the culture for next year.
NOTES: LB Jacquian Williams (concussion) and T James Brewer were ruled out. Brewer missed the entire week of practice, and Jennings missed two of the three days. . Coughlin was noncommittal when asked about shutting down Williams for the season because of repeated concussion symptoms. ''I don't know,'' he said. ''But he's a long way into (the protocol). He's in his third week.'' Williams returned to practice Wednesday, only to miss Thursday and Friday when headaches forced him back into the concussion protocol. ''The symptoms have to be cleared up before there's any opportunity there,'' Coughlin said. ''If he's in a position where he feels good and then he doesn't feel good, the clock begins again there.''. LB Mark Herzlich (concussion) is questionable after returning to limited practice Friday. LB Jameel McClain (knee), WR Preston Parker (knee), DT Cullen Jenkins (calf), CB Dominique Rodgers-Cromartie (back/shoulder), and T Justin Pugh (quad) are probable. . McClain said rattling Titans quarterback Zach Mettenberger will not be easy because of the rookie's innate poise. ''He's pretty good in the pocket against pressure for a rookie,'' McClain said. ''He's pretty accurate, and that's impressive to me. You don't see too many rookies going out there and doing the things he's doing.'' Since making his first start Oct. 26 in place of Charlie Whitehurst, Mettenberger has gone 93 of 155 for 1,287 yards with eight touchdowns and six interceptions. He ranks as the top rookie quarterback with an 87.8 passer rating.
AP NFL website: www.pro32.ap.org and www.twitter.com/AP-NFL