Celtics summer league head coach Jay Larranaga directs his team...

Celtics summer league head coach Jay Larranaga directs his team during the first half of a game against the Philadelphia 76ers in Salt Lake City on July 7, 2015. Credit: AP / Rick Bowmer

Celtics assistant coach Jay Larranaga acknowledged Thursday that he interviewed with the Knicks for their coaching vacancy last week.

Larranaga, who is Brad Stevens’ lead assistant, said the interview with the Knicks took place in Milwaukee between Games 3 and 4 of the Celtics’ first-round series with the Bucks.

“They’re in the middle of their process. We’re in the middle of our process,” Larranaga told reporters at the morning shootaround in Milwaukee before Thursday night’s Game 6. “I appreciated them coming out here. Obviously, all my focus is on the Milwaukee Bucks.”

The Knicks’ process has included interviews with at least eight candidates. Team president Steve Mills and general manager Scott Perry are in Europe, where they met with former Cavaliers coach David Blatt on Thursday, a league source said. After they return to the United States, they’re scheduled to sit down with a ninth candidate this weekend — Spurs assistant coach James Borrego.

But a former Spurs assistant, Mike Budenholzer, might be the most attractive candidate, especially after he and the Hawks mutually parted ways Wednesday night

Because Budenholzer is a free agent, the Knicks, or any team that hires the 2014-15 NBA Coach of the Year, wouldn’t have to give up any compensation for him. A source labeled Budenholzer “a strong candidate” to become Jeff Hornacek’s replacement.

Jerry Stackhouse, David Fizdale and Mark Jackson — three of the first people the Knicks interviewed — are considered serious candidates as well.

The Bucks, Hornets, Magic and Suns also have coaching openings. Budenholzer met with the Suns before interviewing with the Knicks last weekend. He reportedly withdrew his name from consideration for the Suns’ job.

Budenholzer’s unexpected availability means the Knicks or another team will get a coach they likely didn’t have on their wish list when the offseason began. Budenholzer, who spent five years with Atlanta and led the Hawks to four playoff berths, was under contract for two more seasons for roughly $14 million.

It’s hard to imagine that Budenholzer would have left that money on the table if he didn’t believe he could get another job. The Atlanta Journal-Constitution, citing a person with knowledge of the agreement with Budenholzer and the Hawks, reported that what he is owed by Atlanta will be offset by what he earns in his next job.

Budenholzer spent 17 seasons with the Spurs as an assistant under Gregg Popovich and was part of four NBA championship teams. Budenholzer has a relationship with Spurs star Kawhi Leonard, a player the Knicks plan to target in free agency in 2019. Budenholzer also helped Tim Hardaway Jr., one of the Knicks’ cornerstone players, become a better player when the two were in Atlanta.

After the Knicks traded Hardaway to Atlanta in 2015, Budenholzer sent him down to the D-League to work on his game and defense. The Knicks signed Hardaway to a four-year, $71-million contract last summer.

The Knicks also have interviewed Mike Woodson and Kenny Smith.

Larranaga, who was a D-League head coach for two years, is considered a bright young coach with a good pedigree. His father, Jim, is the head coach at the University of Miami, and Larranaga has worked as Stevens’ top assistant for the past four seasons. They reached the postseason all four years.

Stevens praised Larranaga’s basketball IQ and his ability to develop players, which has become a priority for the Knicks.

“He’s super-smart. He works exceptionally hard. He always is looking proactively at projects,” Stevens said. “He’s great with individuals and helping individuals get better. His player development stuff is off the charts.

“As I’ve said about our other guys in the past, I’m just really fortunate to be surrounded by so many people that a) are that capable and work like that, and then b) are totally humble and selfless in their approach. They don’t ask for anything more than to get an opportunity to do their job well.”