Kevin Love was a doughy, nervous 19-year-old in 2008 when he was drafted by the Minnesota Timberwolves.

Six years later, the three-time All-Star could hear his name called on draft night — again.

College stars and international prospects may not be the only ones taking center stage on Thursday night in New York. Love, one of the best big men in the league, headlines a list of veteran NBA players who could have a major influence on how the draft unfolds.

Love’s contract situation has the Timberwolves contemplating trading him, with teams like Boston, Cleveland, Chicago and Denver among those who could use first-round picks as part of a package to acquire him. Orlando’s Arron Afflalo and Golden State’s Klay Thompson could be on the move as well, while soon-to-be free agents like Toronto’s Kyle Lowry and Phoenix’s Eric Bledsoe could have a say in which direction their current teams go with draft picks.

Many of the trades that occur this time of year don’t happen until teams are on the clock and can gauge what players are available to be drafted. Then they can decide whether they can get enough to part with a proven commodity like Love or Afflalo.

“For the most part, the teammates and the coaches will always, always want the certainty of the player in the locker room,” said Isiah Thomas, a former player, executive and coach and current NBATV analyst. “Management will for the most part look at it from a financial aspect, culture aspect and also the type of player they are getting.”

That’s the conundrum the Wolves face with Love, who can opt out of his contract at the end of next season and has made it clear he plans to go elsewhere. Wolves President Flip Saunders could choose to keep Love and try to make roster moves in an effort to convince him to stay in Minnesota. But if he decides to trade him, Saunders has a couple of options:

— He can trade Love for a package of veterans in an effort to avoid a long-term rebuild.

— He could move Love in deal highlighted by draft picks, which could put the Celtics and their two first-round picks on Thursday night — Nos. 6 and 17 — or the Cleveland Cavaliers, who pick first, at the top of the list potential trade partners.

Celtics President Danny Ainge told reporters in Boston on Saturday that keeping their picks was “probably the most likely scenario that happens” and Warriors general manager Bob Myers said Friday that it was “unlikely” they would be involved in a major trade on or before the draft.

But things can change in the blink of an eye.

“I say unlikely because most of the things you talk about don’t happen,” Myers said. “And there’s no blame to be placed. It’s just hard. I mean, it’s hard to make deals in the NBA because it’s very competitive and it has to work for both sides.”

Afflalo had the best offensive season of his career for the Magic last season, averaging 18.2 points, 3.4 assists and shooting 42.7 percent on 3-pointers. But he turns 29 in October, the Magic have a promising young core and are still rebuilding their roster after trading Dwight Howard a couple of years ago.

Meanwhile, the Raptors and Suns have decisions to make with their free agent point guards.

Lowry is coming off of a breakout season and was one of the biggest reasons the Raptors made a surprising surge in the East. But he also figures to garner considerable interest on a free agent market short on playmaking point guards. Toronto has the 20th overall pick in the first round, which is right around where Syracuse point guard Tyler Ennis could be selected and he could provide insurance should the Raptors lose Lowry after July 1.

Suns GM Ryan McDonough has been vocal in his belief that Bledsoe, restricted free agent, will remain in Phoenix and play alongside Goran Dragic, forming one of the most exciting young backcourts in the league.

But over the last month the Suns have worked out several point guards, including Ennis, which would appear to leave open the possibility of Bledsoe or Dragic being traded if the right deal came along. With those players, and a bevy of first-round picks in hand, the Suns could even jump into the Love sweepstakes.

“At the end of the day, the fans will love the lottery and love the potential of the draft pick. However, when that draft pick is not putting up 20 points and getting 10 rebounds, they’re going to hate it,” Thomas said with a hearty chuckle. “They’re going to want certainty. These are the dilemmas that you face.”