As the Knicks’ brass debated whether to stay at No. 3 in the 2019 draft and take RJ Barrett or trade down to pick up another asset, general manager Scott Perry stuck to his instincts.

Legitimate offers were out there, including one from the Hawks, who wanted to send the eighth and 10th picks to the Knicks to move up to No. 3 for Barrett.

Some members of the basketball operations staff thought that could be the route to take: They were unconvinced about Barrett’s athleticism and 3-point shooting and concerned by his inability to use his weak right hand on rumbles to the basket.

“A shooting guard who can’t shoot,’’ one skeptical scout from another organization pondered before that draft.

“Scott kept saying: We have to pick him, we have to pick him,’’ one NBA source familiar with the situation told The Post.

“Him’’ is Barrett, who has made the leap from disappointing rookie season to budding All-Star — while his 3-point shooting and free-throw shooting have drastically improved (32 percent to 39, 61.4 percent to 74.2).

Also Barrett’s skilled and crafty swoops to the hoop are smarter. “Better rim reads,’’ as coach Tom Thibodeau put it. And his cagey defense is a plus instead of a minus.

Even after an inefficient rookie season at age 19, there was still hope Barrett would blossom like spring tulips. When the Knicks met with Barrett multiple times during the pre-pandemic, pre-draft process, they sensed something bigger than his lack of elite athleticism.

“The Knicks saw his intangibles, his mental toughness, strong belief in himself, and his work ethic,’’ another NBA executive said. “He also showed the ability to bounce back from bad plays or bad games with a short memory, perseverance. Those were all important qualities that good NBA players have demonstrated over time.’’

Perry and former Knicks president Steve Mills also looked at Barrett’s pedigree as a high school and college superstar.

“They were betting on his drive to become successful,’’ the NBA executive said. “Failure did not seem an option for him. And he was going to embrace the challenge of playing in New York. He just needed time to learn, grow and develop at this level.”

Last week, Derrick Rose said Barrett is “a perfectionist,” and that could have hampered his rookie season, when the Knicks had no leaders.

During two straight games on the recent 5-1 homestand, Barrett experienced a dreadful first half only to come back with a killer second half each time.

Barrett didn’t easily reverse his misfortunes last season and earlier in this campaign, when he missed 21 straight 3-pointers in late December-early January.

“At halftime, whenever I get a chance, I try to get him, get out of his own head, get out of his own way and let him know, ‘Don’t get frustrated,’ ” Rose said. “He does miss shots … [but] he’s a perfectionist, so whenever I see him down, I try to talk to him as much as possible. And the second half, he came out totally aggressive.”

Is he really a perfectionist?

“Yeah, yeah I am that,’’ Barrett said sheepishly, scratching his face. “I will say that. I hate when everything’s not perfect. I hate missing. If I do everything right and I miss the shot or I do everything right then I turn over the ball, I hate when things aren’t perfect.”

Still, Barrett’s ability to shake off a bad play or a bad half is part of his budding greatness. Even during his dispiriting rookie year, scouts said the kid at least didn’t lack confidence.

When the Knicks drafted Barrett, they also factored in his having a strong father: Rowan Barrett, who had guided his son through his basketball career. Rowan weaved his own accomplished career as a solid St. John’s swingman who played overseas and for Team Canada. The elder Barrett is now GM of Team Canada.

“My dad instilled it in me at a young age,’’ Barrett said regarding not getting down during a game. “It’s a big help because it’s a long game.’’

A player left off both NBA all-rookie teams has those voters eating crow. Two league scouts had a nickname for the Knicks’ high lottery pick — “Boxscore Barrett.’’

In other words, Barrett would pile up points that didn’t affect the game’s outcome, but looked impressive in the boxscore.

In truth, Barrett did not score enough when it mattered last season, but still averaged 14.5 points per game on a 21-45 club. His scoring average is just three points higher this season, at 17.6 points, but he’s making meaningful baskets for the Eastern Conference’s fourth-place team.

Former Knicks coach David Fizdale was so struck by Barrett’s maturity at 19, he played him 35 minutes a game from preseason on in his rookie season.

“I don’t think it was cockiness,’’ said one NBA official close to the Knicks regarding Barrett’s so-so rookie year. “RJ was the third-youngest player in the draft, maybe some immaturity and not knowing the landscape. At Duke, he had Zion [Williamson] and Coach K [Mike Krzyzewski]. He came in and was given too much too early. Now he’s learned from his past lessons.’’

Fizdale said he saw in Barrett a rookie ready to handle a load and wanted to speed his development when he could’ve played veterans.

“It’s really a credit to RJ, Thibs, their staff,’’ Fizdale told The Post of Barrett’s turnaround. “RJ being a helluva pro was never in doubt. He’s got all of the ingredients to be a great winner for years.’’

When several players descend on the team’s Tarrytown facility for night shooting sessions, Barrett doesn’t miss a single evening. Not having promotional appearances this season because of the pandemic could be a factor.

After wearing a flamboyant pink suit on draft night, Barrett flew to Hollywood for the ESPYs the next day instead of meeting with his new coaches.

According to one source, Thibodeau, when he was hired in late July, wasn’t yet sold on whether Barrett knew the work needed to be done to become great. But Thibodeau had a talk with Krzyzewski, and that put him at ease.

“I worked with Coach K with Team USA,’’ Thibodeau said. “So I watched a lot of their games when he played there. Talking to Coach K, I knew the type characteristics he had. I loved his size, I thought he got into the lane extremely well. I knew he was young. With most guys coming in, it takes some time. But just the way he works, who he is as a person, I knew he would improve. We’ll continue to see that throughout his career. Very coachable. Great teammate. He’s had a terrific season and will continue to get better.”

During the Knicks’ win over the Bulls on Wednesday, Thibodeau chewed out Barrett on the bench for consecutive defensive miscues. But scouts watching Barrett see the progress.

One NBA scout who watched Wednesday’s game raved about Barrett’s defensive reads.

On one late-game loose ball, instead of trying to scramble after it, Barrett correctly stayed with his man, Mikal Bridges, who had floated into the left corner. Though that’s the Thibodeau effect, Barrett still executed it in the heat of the moment.

“He’s virtually improved in every aspect of his game,’’ Thibodeau said. “He’s one of those guys that’s young, and I think each game he can learn something, and then he comes in the next day and been a diligent worker.’’

Indeed, from his draft-night pink suit to a yellow hard hat.

“He had all the skills and physical tools to be, at the low end, a good player,’’ another NBA source familiar with the draft process said. “The research showed he was not going to allow himself to fail. With his mental makeup, that would be his floor, but more likely he had the chance to be an All-Star.’’