But the undrafted rookie says he's happy with his progress over the last four games.
The 6-foot-5, 264-pound undrafted rookie had a sack, a fumble recovery, and an interception in last week's win against the Rams to highlight a stretch where he and other youngsters have helped the Giants (6-9) build a three-game winning streak.
With Mathias Kiwanuka likely departing to clear salary space and a decision to be made on current free agent Jason Pierre-Paul, there could be at least one spot open for Wynn. But he is not counting on anything past this year.
''I'm a rookie, so that's not something I really think too much about,'' Wynn said. ''I do my part, do what I can, and worry about what I can control.''
Wynn played 53 of the Giants' 63 defensive snaps in a reserve role behind starter Cullen Jenkins last week, and will undoubtedly see extensive action again in Sunday's finale at MetLife Stadium against the Eagles (9-6), who dropped out of playoff contention last week.
For Wynn, a big showing against Philadelphia would cap his fruitful late-season opportunities. In his four games, he has been credited with 13 tackles and 1 1/2 sacks in addition to the fumble recovery and interception.
That's significant for an undrafted player coming out of Richmond University, a school certainly not regarded as a football factory. His former teammates have been sending their congrats after his latest performance.
''A lot of guys hit me up saying `Keep it up,''' Wynn said. ''The way I represent Richmond, it feels good. It just shines a positive light on my school.''
He's gained a spotlight himself. Wynn chose to sign with the Giants over four other teams, but had not even warranted a game day uniform the first 11 games. It was only because of injuries up front, particularly to veteran Robert Ayers, Jr., that Wynn saw his first action Nov. 30 against Jacksonville.
''I was always confident that if I was put in there, I could go in and make some plays,'' Wynn said. ''But it wasn't time for me to play yet, so I took advantage of getting as much mental reps as I could, and at the same time go in and get an extra workout in, since I'm not playing and getting beat up on on Sundays. I was going to take advantage of the mental aspect as well as the physical.''
Coach Tom Coughlin said it was just a matter of time before Wynn got his chance. Nothing Wynn has done has surprised him.
''Kerry's been with us a long time, all through training camp,'' Coughlin said. ''He impressed us all the way. He just plays hard. He loves to play. He has a unique ability to be in the right place at the right time.''
Coughlin said Wynn has most impressed him with his ability to control his running lane. Yet, he also has the speed and power to collapse the pocket and hit the quarterback. Wynn has three quarterback hits.
Sunday's sack, fumble recovery, and interception lifted his future profile.
''That was being in the right place at the right time,'' Wynn said. ''But it felt good to be in a position to help my team get a victory.''
NOTES: Responding to Rams coach Jeff Fisher's assertion that the Giants bore the bulk of responsibility for last week's first-half brawl that started when linebacker Alec Ogletree took a shot at demonstrative rookie wide receiver Odell Beckham out of bounds, fellow rookie Andre Williams said there was plenty of blame to spread around. ''I don't know who's at fault,'' Williams said. ''I don't think celebrating is any reason for a fight to break out.'' He said he could feel a charged atmosphere on the field. ''I'm not sure what the spark was, but I'm not sure you can point to any one person. There were a lot of bloody hands at the end of it, so I'm not sure.''... RT Justin Pugh on the offense having a better game than the first time around with the Eagles, a 27-0 loss. ''Sure, we have something to prove,'' Pugh said. ''We didn't score at all the first time.''