With up to $33 million to spend — and seemingly as many holes to fill on the roster — the Nets will be looking to strike it big in free agency this summer. And Tuesday they got an up-close look at one of their top targets: Kentavious Caldwell-Pope.

Both scouts and former teammates told The Post that Caldwell-Pope, who had 19 points and four rebounds in a 98-96 loss to the Nets Tuesday, has become the most important piece on a Pistons roster that features All-Star Andre Drummond, and young standouts Reggie Jackson and Tobias Harris. That’s why Brooklyn is expected to make the two-way wing a top priority this summer.

“You can make the argument that he’s their most important player now. So I think that just shows you the impact that he’s had. He’s gone from defender to arguably their MVP,” said Nets guard Spencer Dinwiddie, who was drafted by Detroit in 2014 and spent his first two seasons playing alongside Caldwell-Pope.

“Whenever you can make a leap like that, it shows — especially when you have an All-Star talent like Drummond and Reggie, who last year was putting up numbers that were just shy of being an All-Star.. … So when you have two talents like that, along with what Tobias and Marcus [Morris] are able to do, and then you’re arguably the best player for your team, that speaks for itself.”

Caldwell-Pope, 24, will be a restricted free agent, after he demanded more than $20 million annually and no deal was reached. The Vertical reported Detroit doesn’t want to give him a max contract, but it may not have a choice. The Post has confirmed the Nets’ interest and ESPN intimated they would go that high to get him.

“I’m impressed,’’ Nets coach Kenny Atkinson said when asked about Caldwell-Pope. “I love how he competes, how he competes on the defensive end. That’s really the essence of what I see when I watch him play. He plays with force, he competes on the defensive end.

“On a given night he can get 35 on you easily. His speed off the ball, coming off those [dribble handoffs], flying off and somehow [you’re] going to have to find a way to stay attached, stay close to him.”

Yes, despite averaging 14.2 points and a career-best 37.1 percent from 3-point range, Caldwell-Pope is an inconsistent shooter. And yes, the Nets could have plenty of other targets, from point guard Milos Teodosic to power forward Paul Millsap. But off-guard is the biggest issue.

“I’m not worried about it. That’s up to them. I’ll leave that to the organization and my agent, so I’m not worried about that. I think about basketball,’’ Caldwell-Pope told The Post. “This is what I do. This is my job, so I’m going to play basketball. I’ve got a family to feed.”

The Nets are 28 or younger at every starting position except off-guard, where they’ve been starting 33-year-old Randy Foye, who clearly is not the long-term answer. They offered $50 million last summer to Tyler Johnson, who plays shooting guard. They offered more than $75 million to Allen Crabbe, who plays shooting guard.

Both of those restricted free-agent offer sheets ended up getting matched by those players’ respective teams, Miami and Portland. This summer, Caldwell-Pope will be at or near the top of the market at … you guessed it, shooting guard.

“He’s a guy we can bring back. He’s a restricted free agent,’’ said Pistons coach and president Stan Van Gundy, who is fond of Caldwell-Pope’s defense and team-first demeanor. “KCP, we could bring back. We can’t necessarily have him for sure two years from now, but next year if we want him, we can have him.”

The Nets can offer Caldwell-Pope a four-year, $103 million offer, but Detroit can offer a five-year deal and still not hit the luxury tax. Will the Nets offer, and if so, will they end up like Crabbe and Johnson again?