If the Knicks’ top two coaching desires are Mike Budenholzer and David Fizdale, that doesn’t necessarily guarantee they snare either.

Fizdale has interviewed with Atlanta, Charlotte and Phoenix. And Budenholzer?

Several league sources believe the Bucks and their New York-based ownership will pounce and enter “The Bud Bowl.’’

Milwaukee was eliminated in Game 7 of their first-round series Saturday. At least interim coach Joe Prunty wasn’t fired upon landing at Milwaukee’s airport.

Prunty, who had taken over for the fired Jason Kidd, finished up 21-16 and gained the seventh seed in the Eastern Conference. But a first-round exit against the depleted Celtics isn’t exactly overachieving.

Prunty is not expected back next season. Boston was without Kyrie Irving and Gordon Hayward while missing Marcus Smart for the series’ first four games and Jaylen Brown for the second half of Game 7.

While The Post reported Budenholzer considered the Knicks his “top choice,’’ that was before Milwaukee’s situation crystallized.

One person familiar with the situation said Budenholzer, who interviewed with the Knicks last week, recently talked of preparing a presentation for the Bucks and Knicks.

In addition, Budenholzer considered the Knicks his top choice only before the Hawks fired him on Friday, allowing him to collect all of the $14 million left on his deal.

Sources have indicated an offset clause exists, meaning the Hawks can deduct any salary Budenholzer receives the next two seasons if hired for another coaching job.

Owner James Dolan’s deep pockets aren’t the major factor any longer. The Bucks are not afraid to overpay for the right coach as they make a long-awaited move to a brand-new arena next season.

Their president is former Knicks executive Peter Feigin and they are financed by New Yorkers Wes Edens and Marc Lasry.

The Bucks’ roster is far more accomplished than the Knicks’ group, especially since superstar Giannis Antetokounmpo is close to entering his prime years and Kristaps Porzingis (ACL surgery) may not play next season, at least if you believe Dolan’s remarks to The Post.

If the Bucks re-sign Jabari Parker and he reaches his potential after his own ACL issues, the Bucks should be East title contenders next season with the right guidance.

“Budenholzer and his coaches’ approach to development is top-notch,’’ one NBA source familiar with Budenholzer’s work told The Post.

The Knicks are intrigued with Budenholzer’s Hawks résumé and that the 2015 Coach of the Year turned around Tim Hardaway Jr.’s career, making him an all-around player.

Hawks swingman Kent Bazemore also saw a steep climb under Budenholzer’s tutelage.

Now in his second stint with the Knicks, Hardaway spoke glowingly about Budenholzer.

“I’m just happy he installed that dog and fight inside of me,’’ Hardaway said. “It’s hard to say that, coming into the league you should have that. I kind of lost it. He let me regain it back. I’m very thankful for him for doing so.”

As the Bucks’ future has no limits, the Knicks are destined to be one of the league’s worst teams next season because of the uncertainty around Porzingis’ return.

Knicks general manager Scott Perry said at last month’s season-ending press conference one of their goals for next season is not necessarily winning a lot of games but “winning the 50-50 ball battle.’’

That’s quite a proclamation.

It’s also possible the Bucks have their eye on Doc Rivers, the former Marquette star who hasn’t yet committed to next season with the Clippers despite having one year left on his pact.

According to an NBA source, Knicks president Steve Mills and Perry are not ruling out interviewing an 11th candidate, though no one is on the docket. That could mean Rivers — or Portland’s Terry Stotts — still is on their radar. Stotts is reportedly on shaky ground after getting swept in the first round by the Pelicans.

“I love what I do, but that doesn’t mean that you keep doing it every year. Do you know what I mean?” Rivers said after the season about his future. “I can’t even answer the question.”

Mills and Perry have interviewed 10 candidates and are reviewing their notes and still doing their due diligence. Indications are Budenholzer, Fizdale and European coaching stud David Blatt, whom brass met with in Spain, are at the top of the Knicks’ list.

Meanwhile, fan favorite Mark Jackson has seen his candidacy fail to gain traction.