If there’s a perception Kevin Durant’s decision to choose the Nets over the Knicks was easy, it wasn’t.

Jay Williams, an ESPN broadcaster and Durant buddy, told The Post the free-agent superstar had associates trying to pull him toward Broadway over Barclays Center.

“To give insight, there were people in his camp that wanted him to go to the Knicks,’’ Williams said in a phone interview. “It’s not like: Here’s the Brooklyn Nets and that’s it. Kevin’s his own dude. His relationship with Kyrie [Irving] was the differentiator to the whole thing.”

Williams may have been referring to Durant’s agent/manager Rich Kleiman, a New York resident and Williams’ business partner on the ESPN+ show “The Boardroom.”

Williams also clarified earlier comments he made on a podcast suggesting Durant would have given more consideration to the Knicks if they hadn’t traded Porzingis.

Williams said he was parroting a conversation on Stephen A. Smith’s radio show in which Smith brought up Durant nicknaming Porzingis “The Unicorn’’ and perhaps wanting to play with him.

Williams said it was no factor.

“It was something Stephen A. said earlier, and I referenced it,’’ Williams said. “I don’t think it had anything to do with Porzingis. It was not the difference-maker with the Knicks and Kevin.”

Williams said he believes Durant did not want to pass on an opportunity to live in New York and unite with Irving like they did on the 2016 Olympic team. The Porzingis trade opened up that possibility. Williams disputed owner James Dolan played a role.

“I think they’re more than friends,’’ Williams said of Durant and Irving. “ They’re like brothers . It’s not just like, ‘Hey we’re a friend.’ That relationship to him is very special. In the culture of basketball, people are trying to tear you apart and go different ways. They took the journey they had and they really understand each other. It came down to his relationship with Kyrie. It was a difference-maker, man.”

Williams can’t say if Durant would have been more emboldened to join the Knicks solo if he didn’t rupture his Achilles tendon and have Irving as a crosstown rival.

As much as Williams says the “Knicks, Nets, Golden State were really, really there on the table,” it sounded like New York’s teams were the front-runners.

Something that happened in 2014 fortified Williams’ belief Durant would one day play in New York. Durant has long talked about his historic night at Rucker Park during the 2011 lockout when he rang up 66 points before a frenzied crowd on 155th Street.

Three years later, Williams witnessed another moment when he, Kemba Walker, Kent Bazemore, Will Barton and David Lee were to play at Rucker Park. The match got rained out and moved to Harlem’s Riverside Church.

“It felt like an old-school, crazy high school game — people on the court yelling, talking trash, hyping us,’’ said Williams, whose NBA career was derailed by a motorcycle accident. “There was a love I saw in Kevin’s eyes, and I felt it too. That’s what I missed about the game.

“He saw there’s something special with the energy that comes with being here. There’s a love for hoopers. If you’re a hooper and care about the nuances, the angles of attack and trash-talking, the passion, that’s what that presented to him. It’s who he is at the root.”

Durant, likely to miss next season, will have to hope for that frenzied feeling at Barclays — where the Nets posted the NBA’s worst attendance last season.

“He’s been here since he got hurt,’’ Williams said. “He does love it here. The Nets have pieces and with [GM] Sean Marks and what he’s been able to do. Spencer [Dinwiddie], Deandre [Jordan], Caris Levert, Jarrett Allen. All those pieces aligned with where he wanted to go.

“I never heard Kevin speak about Jim Dolan. Kevin loves to focus on basketball. He’s a basketball savant. What’s the best place for me to hoop? Expectations were set high by Dolan on [Michael Kay’s] show. But they’re doing it the right way. Keep expectations low and keep building.”

In the first 20 hours of free agency, the Knicks signed six players — just one known starter in power forward Julius Randle. The other signings — all one-and-one team option deals — were Elfrid Payton, Bobby Portis, Reggie Bullock, Taj Gibson and Wayne Ellington.

Their work ethic and short-term nature of the deals struck Williams as the Knicks’ best alternative following the Durant snub.

“There’s a workmanlike mentality they all have,’’ Williams said. “[Coach David Fizdale] likes that. It’s his style. So they will pay you for one year, though the money seems absurd, but it’s a team option if they want to continue that. Which I think is brilliant on their part. Let me rent for a year and see what that free agency looks like. You want Kevin Knox, RJ Barrett, Dennis Smith around guys like that who bring that mentality every day.’’