Let the J.R. Smith Sweepstakes begin!

As NBA free agency begins Sunday night at midnight, the success of the Knicks’ July will hinge on whether they keep their own free agents as much as bringing in new blood, as Smith, point guard Pablo Prigioni and forward Chris Copeland all could fly the coop.

Regardless of Prigioni’s situation, the Knicks are bent on adding another point guard because of Jason Kidd’s retirement. The Pistons’ Will Bynum, Brooklyn’s C.J. Watson and and Atlanta’s Devin Harris are on the radar.

The Knicks also want to add a backup big because of Amar’e Stoudemire’s uncertain health. Two local products, Elton Brand and Lamar Odom, are targets. The Knicks also will entertain re-signing Kenyon Martin.

Problem is, the Knicks have just one $3.19 million mini mid-level exception to spend and the veteran’s minimum of $1.4 million to sign free agents. They conceivably could have to use a portion of the mini-midlevel to retain Prigioni or Copeland. The new collective bargaining agreement has put them in a giant hole, because they no longer can obtain a free agent via sign-and-trade because they are over the luxury-tax threshold.

According to a person who spoke to Smith, the explosive but flaky shooting guard believes he will get an offer that will top the Knicks’ maximum bid — starting at $5.4 million — under early-Bird-rights bylaws.

The Sixth Man Award winner who flopped in the playoffs then must decide if he wants to take a little less to stay in his hometown and perhaps play alongside his brother, Chris Smith.

The Knicks believe odds are they will retain J.R. Smith, but it hardly is a guarantee considering the bevy of under-the-cap clubs and a weak free-agent class. The Bucks, Pistons and Suns are contemplating throwing money Smith’s way.

The Knicks are resigned to the notion Copeland will take the money and run. He is coming off a minimum contract of $472,000 and is seeking “Steve Novak money’’ — four years, $16 million. The Pelicans will make a run at Copeland, as reported by The Post. The Pacers also have interest, as do the under-the-cap Mavericks and Bucks.

For a team with so-called championship dreams, there are many question marks and Knicks general manager Glen Grunwald admitted there are “needs across the board,’’ including a point guard, a big and another wing player.

Former Knick Shawne Williams worked out last week and is a candidate for the vet’s minimum to replace Copeland. The Knicks also like shooters Mike Dunleavy and Marco Belinelli, but their priority for the mini-midlevel is a point guard.

The Knicks may be active on the trade market. If they lose Copeland in free agency, they are permitted to work out a sign-and-trade and perhaps can get back a trade exception. They could then use that trade exception to deal for another player. They are also not averse to trading 3-point specialist Novak.

But Smith is the key to everything. He remains their secondary scorer to Carmelo Anthony and they may have to sell him on a starting berth for him to re-sign. Smith wasn’t happy to be Sixth Man but it worked. If he gets a huge deal elsewhere, it likely would be to start.

Smith said after the disappointing ending he wanted to “retire a Knick.’’ But the day after the Knicks drafted shooting guard Tim Hardaway Jr., Smith teased on Twitter: “It was fun while it lasted.’’ He later tweeted he was referring to his cab ride.

Other teams may be hesitant to sign Smith to a long-term contract, given his poor playoff resume and his motivation should he land a multi-year deal. Smith told The Post last season he believes he should be in the conversation for All-Star status. His chances of making that happen would be best under the bright lights of New York.

Prigioni’s situation is mysterious. The Knicks would love if he could sign for their qualifying offer of $940,000 if no other team steps up. But he is 36 and is considering returning to the Spanish League if he doesn’t get bowled over.

Prigioni, who could be averse to trying another city and moving his wife and young children, could even have a starting role here if Woodson returns to the two-point-guard alignment, but the Knicks prefer not to dip into their mini-midlevel to keep him.

Bynum is the Knicks’ top point guard priority, but he could re-sign with the Pistons, with fellow Chicago native Maurice Cheeks now head coach.

marc.berman@nypost.com