No, Phil Jackson didn’t exactly throw money Steve Kerr’s way early on in the process of seeking a new Knicks head coach. By the time Jackson’s offer improved, it was too late.

The Post has learned Jackson’s initial offer to Kerr was a lowball of three years, $13.2 million. That offer stuck for more than a week before the Warriors got involved Tuesday. Kerr wound up agreeing to terms with Golden State on a five-year, $22 million contract — not the $25 million that was widely reported.

Had the Knicks originally offered Kerr five years, $22 million — $4.4 million a year — he probably would have closed the deal before Golden State could reenter the fray. Jackson only bumped the offer to four years in response to Golden State’s offer.

A source said Kerr wasn’t moving across the country for less money than the Warriors were offering. The Knicks have insisted Jackson, not owner James Dolan, handled the negotiations. Kerr never spoke to Dolan during the process, meeting with general manager Steve Mills and basketball operations director Jamie Mathews.

The Warriors had preferred Stan Van Gundy, who wound up in Detroit.

“I think Steve is a very bright guy who knows the game inside-out,’’ Van Gundy told The Post. “He’s very intelligent, got a great demeanor. There’s always adjustments when you go into a new job. He’ll have adjustments to make but he’s a bright guy.’’

A source said Jackson wants Tim Hardaway Jr. to play in the Las Vegas summer league despite his solid rookie season, in which he finished fourth in the Rookie of the Year voting. Hardaway did well at last year’s Chicago combine, but still fell to No. 24 in the draft.

“I was proud of his whole season,’’ said his father, Tim Hardaway Sr., who was at the combine as a Heat scout. “He exceeded everyone’s expectations. I was very happy for him. He’s still learning, still has work to do.’’

Hardaway said of his son’s combine performance: “He shot the ball very well, went through skills very well. He improved his stock, but a lot of people didn’t know his basketball IQ and everything he could do, so it didn’t matter.’’