The Knicks are moving closer to naming Jeff Hornacek as their next coach.

According to a league source, the Knicks have offered their coaching job to Hornacek. Contract talks have begun between the two sides and they’re progressing.

“Nothing is done,” the source said. “Are they going to work it out? It would be astonishing if they didn’t.”

Nothing was expected to be finalized Thursday, but Hornacek was at the Knicks’ training facility in Westchester, multiple NBA sources said.

After a slow start to the Knicks’ coaching search, things picked up steam this week. Team president Phil Jackson interviewed Hornacek in Los Angeles Monday. On Wednesday, Jackson and general manager Steve Mills had dinner with Hornacek in New York.

Hornacek was 101-112 in 2 1⁄2 seasons with the Suns. He finished second in Coach of the Year voting after guiding Phoenix to a 48-34 mark in 2013-14. Hornacek was let go in February when the Suns were 14-35.

At his end-of-season news conference in April, Jackson said he would interview “only people I probably know” and he wanted “someone who has compatibility with what I do as a leader and would have to be in sync with what we do.” Jackson and Hornacek have never worked together before.

Jackson interviewed former Cavaliers coach David Blatt, former Pacers coach Frank Vogel and Warriors assistant Luke Walton, who took the Lakers’ coaching job.

It was speculated that interim coach Kurt Rambis would be given the job on a full-time basis, especially after he and Jackson ran a two-day triangle seminar/minicamp for Knicks players a week after the season ended. They’re also close friends.

But Jackson went a different route, and picked Hornacek, the former shooting guard whom Jackson liked as a player.

It remains possible that Rambis will stay on with the Knicks in some capacity, perhaps as an associate head coach. Hornacek and Rambis were teammates with the Suns in the early 1990s. Rambis also could work with Jackson in the front office.

Hornacek played and coached under Hall of Famer Jerry Sloan in Utah. Hornacek’s first NBA coach in Phoenix was Cotton Fitzsimmons, who was an assistant under Tex Winter at Kansas State and ran some principles of the triangle. So Hornacek has familiarity with the triangle, but he didn’t coach it with the Suns.

In Phoenix, Hornacek used a two-point guard system that worked well since he had Eric Bledsoe, Goran Dragic, Isaiah Thomas and Brandon Knight running it.

The Suns often played small. They attacked teams in transition, and early in the shot clock, utilizing drive-and-kicks and were a high-volume, three-point shooting team. Phoenix averaged 105.2 points and was eighth in offensive rating (points per 100 possessions) in 2013-14. They were 11th the following season, playing small and quick again. But bad trades and injuries hurt the Suns, and ultimately cost Hornacek his job.

The current Knicks’ personnel doesn’t fit that style, which is far different than the triangle. The Knicks usually played big and were half-court oriented.

In the two seasons they utilized the triangle under Derek Fisher and Rambis, the Knicks averaged 91.9 points in 2014-15 (last in the league in offensive rating) and 98.4 points this past season (27th).

Hornacek could go back to Sloan’s bread-and-butter of pick-and-roll that made John Stockton and Karl Malone all-time great players. Hornacek spent three years as a Jazz assistant, including half a year under Sloan.

The Dolan family owns controlling interests

in the Knicks, Madison Square Garden and Cablevision.

Cablevision owns Newsday.