Odell Beckham Jr. wanted something to help him remember the games. Keepsakes, so to speak. So after each of his NFL games he's gone up to an opposing player and asked him to swap jerseys. He did it with Dez Bryant of the Cowboys, Colin Kaepernick of the 49ers and Richard Sherman of the Seahawks. Others, too.

Some people go home from NFL games with foam fingers or other souvenir-stand merchandise. Beckham goes home with a jersey that is not only game-worn but worn in a game in which he played.

"It's usually one of those things where you talk to a guy after the game, 'What's up? Do you want to trade jerseys?' " Beckham said. "It's just a way of you remembering the game and another player that you respect. It's that type of thing . . . You see it in the NFL a lot more now."

But the dynamic of what started out as a rookie receiver offering his uniform for one from a higher-profile player is beginning to change.

Now Beckham is the budding superstar. He's the one with the highlight-reel catch -- book this man a ticket to the ESPYs, ASAP! -- and the million-plus Twitter mentions and the bright future. So it probably won't be long before Beckham stops doing the asking about the jersey exchange and players start lining up to snag some of his gear.

"If they want to trade, I'll definitely trade," he said. "Add to the collection."

Beckham takes the field on Sunday for the first time since he became an Internet immortal.

He and the Giants (3-8) are facing the Jaguars, a 1-10 team that hasn't garnered as much attention all season as Beckham has in the past week. With both teams out of playoff contention, there's very little juice to be squeezed from the matchup. About the only thing that might be worth tuning in for is the answer to the question: How is Beckham going to top himself?

"I feel like you just keep doing the little things right," he said. "Obviously, a receiver is supposed to catch the ball with two hands, so any time the ball's coming your way, catch the ball and just keep continuing to get better each and every day."

Beckham can't help himself when it comes to dazzling. At Friday's practice, he spun a football on its end at the 20-yard line, backed up and kicked it through the uprights for an unassisted 30-yard field goal. He also caught a football one-handed -- which has become routine for him -- and then threw it into a basket that quarterbacks use to improve their accuracy.

From about 30 yards away.

There's even a way fans can wager on whether Beckham will make another one-handed catch in this game. The odds, courtesy of Bovada, are 7-to-1 that he will.

"I didn't even look into that," Beckham said at the example of the absurdity of it all. "I wouldn't bet on it if I were y'all."

It's almost hard to remember just a few months ago that some people were calling Beckham a bust before he had even played a snap.

He had a hamstring injury that forced him to miss all of training camp and the first four games of the regular season. Coach Tom Coughlin grumbled about his unavailability for practices, and when he finally did take the field, no one was really sure what he would be able to bring to the team because he hadn't practiced.

"I definitely expected to have a good season, but I didn't know that it would be going the way that it is," Beckham said. "It's a good feeling to be able to finally put the hamstring and all the other stuff that was around it behind you and just move forward."

After Sunday's game, the players for the Giants and Jaguars will meet on the field and shake hands and move on to the final four games of their arduous seasons. College and high school teammates will catch up with each other. Former NFL teammates will check in. And there might even be some jerseys exchanged.

This time, though, the interesting part won't be looking to see which player's jersey Beckham winds up with. Instead, it'll be who gets Beckham's.

Kiwi out. Defensive end Mathias Kiwanuka (knee) was downgraded Saturday from questionable to out and he did not travel with the team. Robert Ayers Jr. will likely start in his place and Damontre Moore should see more snaps too. Right tackle Justin Pugh (quad) did make the trip with the team after missing last week's game. His status remains questionable.

With Colin Stephenson