Apparently Jason Kidd isn’t satisfied with just coaching the Nets, and it may cause him to leave the franchise.

A league source told The Post Kidd recently approached ownership with a series of demands, including the role of overseeing the Nets’ basketball operations department in addition to his head-coaching responsibilities. The source said Kidd didn’t want general manager Billy King to be dismissed, but wanted to be given a title and placed above him in the organizational hierarchy.

Ownership declined to grant Kidd that kind of power, which is rare for any coach in the league to have. The source said ownership felt Kidd wasn’t ready for that kind of responsibility after having only one year of coaching experience — the team finished his first season on the bench with a 44-38 record, good for sixth in the Eastern Conference — and allowed Kidd to seek other opportunities.

The franchise then was asked by the Bucks for permission to speak with Kidd about the prospect of hiring him and the Nets consented, making his departure from Brooklyn a sudden possibility. According to reports, the two teams already have been discussing possible compensation to release Kidd from the final three years of his original four-year, $10.5 million contract.

Kidd’s compensation has been dwarfed by Derek Fisher and Steve Kerr this offseason, who both received five-year, $25 million deals.

Bucks coach Larry Drew just completed his first season in Milwaukee after the team hired him last summer following his contract expiring with Atlanta. Neither Drew nor the Bucks front office was aware Kidd would be interviewing, according to reports.

“We’re not going to comment on rumors or speculations,” the Bucks said in a statement.

Kidd did not immediately respond to a request for comment.

The Bucks, long one of the league’s moribund franchises, has been injected with new life after the sale of the team from its longtime owner, Sen. Herb Kohl, for $550 million in mid-May to New York investment firm executives Marc Lasry and Wes Edens.

Lasry, who is a good friend of Kidd, previously owned a small stake in the Nets.

Milwaukee selected Duke star Jabari Parker with the second overall pick in Thursday’s draft at, ironically, Barclays Center in Brooklyn, pairing him with rookie Giannis Antetokounmpo to give them two exciting young forwards to build around.

Holding the dual roles of both coaching a team and overseeing basketball operations is rare in the NBA, with only San Antonio’s Gregg Popovich, Detroit’s Stan Van Gundy, Minnesota’s Flip Saunders and the Clippers’ Doc Rivers currently holding both roles. Van Gundy and Saunders assumed their roles this offseason.

The Nets hired Kidd last June less than a month after he retired from his stellar 19-year Hall of Fame career in which he spent six-plus seasons with the franchise, leading them to a pair of Finals appearances and establishing himself as the best player in the franchise’s NBA history.

Kidd endured a rocky start, including a 10-21 record through the opening two months of the season and the “re-assignment” to filing daily reports of assistant coach Lawrence Frank — who had signed a six-year contract worth roughly $1 million on average last summer after being pursued by his former point guard with the Nets. Kidd turned things around after the start of 2014, leading Brooklyn to a 34-17 record from Jan. 1 through the end of the regular season.

The decision to swap out Shaun Livingston for Alan Anderson in Games 6 and 7 was a deciding factor in the Nets’ comeback from a 3-2 first-round deficit against the Raptors to advance to the Eastern Conference semifinals, where they eventually lost to the Heat in five games.

Kidd was on hand at the unveiling of the site of the team’s new practice facility in Brooklyn on Thursday, and spoke at length about the state of the franchise. He expressed a desire for the franchise to re-sign free agents Paul Pierce, Shaun Livingston, Alan Anderson and Andray Blatche.

He also said he would be with the team this week in Orlando, where the Nets’ Summer League team will begin practicing ahead of its first game Saturday morning. Unlike last summer, however, when Kidd coached several games, he said assistant coach Sean Sweeney would run the team.