There are times when Prince Amukamara not only looks wide-eyed but he acts it as well, as if he’s somewhat amazed and perhaps even a bit baffled by his surroundings.

“I think he does it just for attention, to be honest with you,’’ teammate Terrell Thomas said yesterday. “He’s smarter than people think. At the same time he has to lose that little kid sense. Become more of a professional. He just turned 24, third year in the league, first-round pick, he has to pick up the production and be a leader.’’

As veterans and cornerbacks, Thomas and Corey Webster have leaned on Amukamara, demanding that he pick up the pace of his NFL progress. Do more. Expect more. It hasn’t been a particularly smooth or swift ascension for Amukamara with the Giants, but in his mind he’s on the precipice of fulfilling his potential.

“I want to be the No. 1 corner on this team,’’ Amukamara said after the Giants went through a brief walk-through and then parted ways until training camp. “I feel like right now Corey is and my goal is to always just try to beat him out, and I think as soon as I establish myself as the No. 1 corner then hopefully become the No. 1 corner in the whole league.

“I know that’s going to take work but I mean, guys that came out of my drafting class are doing great, Patrick Peterson and Richard Sherman, those are the guys I kind of compare myself to. I’m just trying to exceed all of them, I guess.’’

No one is uttering Amukamara’s name with the best corners in the league, but the Giants would like to think he can rise near the top of the pack. They had Amukamara ranked considerably higher than No. 19, and they could not believe their good fortune when he was sitting there at that spot in the 2011 NFL Draft. The lockout cost him the offseason in his rookie year, a broken left foot limited him to seven games as a rookie and an injection to quiet down the foot kept him on the shelf for last year’s off-season workouts.

Nowadays there are no health issues with Amukamara and he has managed to keep from getting dumped into a cold tub, which shows he’s gaining some respect inside his own locker room. But there’s more work to be done.

“I think he’s still a little wet behind the ears as far as his mentality, how he attacks his daily job,’’ said Thomas, who is attempting to return from a third ACL surgery on his right knee. “Me and Corey have been working on him with that, letting him know just doing your job is not enough, we need more out of you. I think he’ll get it. Sometimes it takes some people a little longer than others.’’