NEW YORK — When teams dangle veteran stars for prospects this offseason, Yankees general manager Brian Cashman will do his best to say no.

New York missed the playoffs for the third time in four years and at 84-78 finished four games out of an AL wild card.

The Yankees struggled to a 9-17 start, then improved in the final two months of the season after bringing up catcher Gary Sanchez, right fielder Aaron Judge and first baseman Tyler Austin.

First base prospect Greg Bird, a late 2015 sensation, returns following shoulder surgery, and more youth could bubble up from the minors during the season.

Right now, a veteran pitcher such as White Sox ace Chris Sale probably is not a good fit for the rebuilding Baby Bombers.

“We have an exciting, young nucleus that’s coming, Some of it’s arrived, some of it’s still coming,” Cashman said Wednesday.

“You’d have to be one piece away, and I would not recommend that type of decision-making as we approach the 2017 season. I think that would be a dangerous approach.”

Cashman spoke for nearly an hour, assessing 2016 — “our offense was bad; we had a bad offensive team” — and detailing his approach for 2017. He anticipates competitions among young players for first base and right field during spring training.

“There will be some hesitancy to forego giving the kids a chance to take it, and certainly that can create some problems if they don’t,” he said. “But that doesn’t preclude me from being open-minded to any and all opportunities that present themselves.”

Seven years removed from its last World Series title, the Yankees traded Aroldis Chapman, Andrew Miller, Carlos Beltran and Ivan Nova for prospects during the summer and released Alex Rodriguez.

They cut payroll to roughly $224 million and saved $2.38 million in luxury tax in the process, but still will pay about $26.5 million.

Yankees average home attendance dropped from 41,995 in Derek Jeter’s final season in 2014 to 39,430 last year and 37,820 this season.

Average viewers on the YES Network fell from 288,000 in 2014 to 259,000 the following year to 218,000 this season — Mets’ games on SNY averaged 263,850 this year, up from 242,667 in 2015.

“They wanted us to press that reset button and in many cases tired of seeing what was transpiring in the first few months of this year, the been-there, done-that, it’s time to do something that was not part of our DNA,” Cashman said.

He likened this period to the late 1980s and early 1990s, when the Yankees failed to make the playoffs until a renaissance led by Jeter, Mariano Rivera, Andy Pettitte and Jorge Posada.

“I remember when I was the assistant farm director while we were collecting a lot of the talent like what we collected,” Cashman said. “Who knew we were actually sitting on a dynasty waiting to happen? None of us.”

Cashman also:

— anticipated he and Girardi would go through the final seasons of their contracts in 2017 and ownership will then decide after the season whether to offer new deals.

— wants to reach a new deal with pitching coach Larry Rothschild; the other coaches are signed through 2017.

— even though Gary Sanchez has supplanted Brian McCann as the starting catcher, he envisions a role for McCann as a backup catcher and designated hitter. “But that doesn’t preclude me from listening (for a potential trade), either.”

— views Luis Severino as starting pitcher but is concerned about a sophomore slump that resulted in a 3-8 record and 5.83 ERA. “If you’re a student you go back and do your homework to brush up for your test, so you can master the next test. He was unable to do that from the starting spot all year long.”

— said pitcher CC Sabathia will have what is expected to be minor surgery on his right knee within the next week.