GREENBURGH, N.Y. — Jeff Hornacek said he really had no “connections” to Phil Jackson and was surprised when the Knicks’ president wanted to interview him for the team’s coaching vacancy. But the two apparently connected right away.

Jackson said he quickly felt comfortable with Hornacek and was impressed with his basketball knowledge and philosophies. They met for six hours in Los Angeles a little more than two weeks ago, for another six hours on their flight to New York and for six more hours the next day. The triangle offense was a big part of the conversation and will remain a big part of how the Knicks play.

When the meetings ended, Jackson gave Hornacek a three-year deal to coach the Knicks, which is what’s left on Jackson’s contract as team president. So Jackson, whose record as a president is 49-115 with no playoff appearances, has linked his legacy as an executive to Hornacek.

“Knowing him as a competitor, as a player and as a coach, the demeanor, are things I liked about Jeff,” Jackson said during Hornacek’s introductory news conference Friday at the Knicks’ training facility. “He’s a person that you can relate to, and it’s one of those things that was just right off the bat. The communication level went on forward from there.

“That comfort zone was possible and that basketball knowledge that he has and the familiarity he has with playing basketball are things that attracted us to Jeff.”

Hornacek, 53, has a good basketball background. His father, John Hornacek, was a high school coach, assisting at St. Josephs High School when Isiah Thomas, now 55, played at the suburban Chicago school. Jeff Hornacek, who went to a high school in the next town, played pro ball for Cotton Fitzsimmons and Jerry Sloan and was an assistant under Sloan in Utah.

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As a head coach, Hornacek was 101-112 in 2 ½ seasons with the Suns coach before being fired in February.

Jackson said he had a relationship with Hornacek from the 1990s. His Bulls tried to acquire Hornacek, as did the Knicks in 1994. Hornacek ended up with the Jazz and lost to the Bulls in the Finals in 1997 and 1998.

But Hornacek said he never really had spoken to Jackson before their initial sit-down in Los Angeles about three weeks ago, which coincided with Hornacek’s daughter’s graduation from USC.

Hornacek said he never thought coaching the Knicks was a possibility. “I really didn’t think it was,” he said. “When my agents called and said Phil is going to call you, [I was like] “Really?” I was pretty surprised. I think probably the only words I ever said was, ‘Congratulations on the championship again’ when they beat us the two times. So I really didn’t ever talk to him a lot prior to that. So going into the meeting, I’m like, OK, this will probably be an hour or two that I’ll talk to him.”

But they talked much longer, and over several days.

“I am not sure if I have talked that much in my life,” Hornacek said, adding that he also met with Knicks general manager Steve Mills. “So it was very easy to talk basketball, talk philosophy and getting to meet Steve. It just fit for me and I was hoping it fit for them. I think it is going to be a great collaboration between us.”

Hornacek favors an up-tempo game and the use of pick-and-rolls, and he plans to run that with the Knicks. But he wants to blend his system with the triangle offense, and he joked about changing the name.

“There must be something about the word triangle,” Hornacek said. “Maybe we’ll call it the circle offense. When I was talking with [Jackson] in L.A. and we started looking at things that I wanted to do out of the triangle offense, he goes, ‘Yeah, you can run every play that you want out of the triangle offense.’ ”

Jackson’s affinity for the triangle is why interim coach Kurt Rambis was thought to be the favorite for the job. Jackson said Rambis was “strongly considered,” and Hornacek has talked to Rambis about staying on as an assistant coach.

Hornacek said he will speak with the assistant coaches remaining from former head coach Derek Fisher’s staff and decide quickly on their futures as well as whom he wants to add to the bench. Hornacek said he’s considering keeping Rambis, his former teammate on the Suns.

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“I think it’d probably be more awkward if I didn’t know Kurt,” Hornacek said. “But I do know Kurt and we talked about a lot of things and how, if I kept him on as coach, what his role would be. It was a good talk.”

The Knicks have several roster issues to address, but having Carmelo Anthony and Kristaps Porzingis gives them a chance to return to the playoffs.

“We have a lot of good pieces,” Hornacek said. “I think it’s always a goal to get in the playoffs. It’s been a couple of years, but going into the season, that’s going to be the goal for our team: to get back in the playoffs.”