Prince Amukamara says he wants to return to the Giants next season.

Whether the feeling is mutual will determine if that happens.

Tom Coughlin said the cornerback has been “a little bit up and down” in his play since coming back from a pectoral injury that kept him out for five games. That he’s played 16 games in a season only once in his career also could be of concern to the Giants as they decide whether to pay the former first-round pick top cornerback money. If they decide not to, he could be one of the top players on the market at his position and cash in elsewhere.

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“I think any first-round draft pick or draft pick would love to stay where they were drafted at, unless they just had a horrible experience, and that definitely hasn’t been my case here,” Amukamara said. “I love the organization, definitely treated first-class here, so it’s been great.”

The Giants have not signed one of their former first-round picks to a multiyear contract after the culmination of his rookie deal since they gave Mathias Kiwanuka a two-year “prove it” deal coming off a neck injury in 2010. Before that, you’d have to go back to Jeremy Shockey for the last first-round pick to receive a significant second deal from the Giants.

That might be more a reflection on the Giants’ selection process than the players themselves.

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Amukamara and defensive end Jason Pierre-Paul, who also is a free agent-to-be after playing under a modified franchise tag during the second half of this season, are looking for long-term commitments and would like to be back with the Giants. And both have been honest about the possibility that Sunday will be their final game in a Giants uniform.

“I don’t know if I’m going to be a Giant next year, so I’m going to give it all I got in this last game,” Pierre-Paul said earlier in the week. “Put it all on film and let it take care of itself.”

As with Pierre-Paul, the Giants do not appear to have Amukamara’s replacement in waiting on the roster. Dominique Rodgers-Cromartie is the other starting cornerback, and if the Giants part ways with Amukamara, they’ll have to bring in a starting-level free agent or use one of their earliest draft picks to land a plug-and-play rookie.

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Amukamara admitted that he has been thinking about his future, really since he came into this season without any murmurs of a pending extension.

“It’s always been in the back of my head,” he said. “I think when there were no talks before the season, I was planning on just focusing on the season and playing this season out, not expecting anything, and that’s been the case. The main focus is to finish the season.”

There are, of course, plenty of variables. Will Coughlin’s future play a role in Amukamara’s decision? Would he take less money to stay? Is he more interested in cashing in on a potentially big payday or playing for a team he sees as a contender?

“These are all the questions I haven’t thought about yet,” Amukamara said. “I’d have to think about it.”

So will the Giants.

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