Damon Harrison sounded as if he were preparing to take on a division rival, or even a playoff opponent.

“We don’t want to give them anything,” the Giants defensive tackle said with as much of a snarl as his perpetually grinning face could muster. “They’re not getting a thing. They have to earn it.”

A few things about those statements. First, it’s May. Second, it’s organized team activities, or OTAs, and the players aren’t even wearing equipment beyond helmets. And third, he was talking about his own teammates.

If the first three practices of OTAs this past week are any indication of the mindset of the Giants’ defense, the unit should have no problem living up to coordinator Steve Spagnuolo’s mantra of staying hungry. Never mind that before each video session, Spags reminds them of that directive, tells them that “iron sharpens iron” and harps on them to forget about last season’s successes. Even without that message, these guys show no signs of pacing themselves for the long haul of the 2017 season or resting on past accomplishments.

They were breaking up passes, thumping ballcarriers and trying to wrestle away fumbles, and they got into a shoving match at the line of scrimmage with the offensive linemen. Harrison, all 350 pounds of him, even dived to make an interception on a pass that was tipped by Jason Pierre-Paul.

“I think that everyone has a chip on their shoulder,” cornerback Janoris Jenkins said. “An even bigger one than last year, knowing that we understand the scheme and the situation, so we just have to come out here and get better.”

How much better can they be? Jenkins said he’s not thinking about rankings or statistics. “That’s just something that you put on a piece of paper and you see a number,” he said.

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No, the real measure of their progress will come from a more subjective perspective.

“I think we are going to be special,” he said.

They seemed pretty special last year when they made the jump from the worst defense in the league in 2015 to a top 10 unit that essentially drove the team to the playoffs.

“We were OK,’’ Jenkins said of the 2016 defense. “It was our first year. Everybody’s first year together and I feel like we have that bond and chemistry where I know how [Landon Collins] plays, he knows how I play. I know how [Olivier Vernon] plays at the d-end, what they expect on the other side of a tight end. It is just things like that and paying attention to details.”

And not being satisfied.

That could have been a challenge for players such as Harrison and Jenkins, who played in relative obscurity early in their careers and emerged as stars for one of the NFL’s marquee franchises a year ago. Now they have labels such as “All-Pro” and “Pro Bowler” attached to their names. They’ve gotten their first taste of postseason football.

Judging by Harrison’s reaction to being named one of the top 100 players in the NFL last season, staying hungry will not be an issue.

“[Ninety-six] on the top 100 is pure disrespect,” he wrote on Twitter earlier this month. “95 other players better than me? . . . Nobody is safe.”

“Anything from last year, don’t expect that this year,” Jenkins said. “It’s just like we have to start all over again and keep building to get better. You can’t depend on paperwork from last year or plays that we made from last year because it is a new year.”

There’s only one more thing to do.

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“Be the best defense we can possibly be,” Jenkins said. “We just want to get that fifth trophy in the case.”

And if that means roughing up their teammates a bit in May, well, so be it.