Former Knicks coach Mike Woodson chuckled when he was told David Fizdale had an interview scheduled next week with president Steve Mills for the team’s open head-coaching job.

“I gave him his first job in Atlanta,’’ Woodson mused about hiring Fizdale in 2004 — though Fizdale worked as a Warriors assistant under Eric Musselman the prior season.

Contacted by The Post on Saturday, Woodson said he hadn’t heard from the Knicks yet, but would love to.

Woodson, who has been Doc Rivers’ top assistant with the Clippers the past four seasons, was the Knicks’ most successful head coach since Jeff Van Gundy, guiding them to their most recent playoff berth, in 2012-13, when the club posted a 54-28 record.

“I don’t want to hide the fact I’d love to be back,’’ Woodson told The Post in a phone interview. “I’d like to finish what I started. At the end of the day, you want to come to New York, based on my body of work there. I want it to be mutual. I want them to want me. I hope they call me.’’

Mills and general manager Scott Perry sound as if they are open to a young coach they can mold more than someone with Woodson’s veteran credentials.

“I think in New York, it’s better to have done this before,’’ Woodson said. “You can ask Derek Fisher that. I like New York, but New York is a tough place to coach.’’

Fisher replaced Woodson in 2014-15 and flopped. Woodson had worked with Mills for one season in 2013-14 and Perry in Detroit as an assistant coach.

Woodson, 60, was fired by then-Knicks president Phil Jackson following the 2013-14 season — without a meeting — after the team missed the playoffs by one game. He finished with a Knicks career record of 109-79.

Woodson joined Rivers in Los Angeles and the Clippers were title contenders until just falling short of the playoffs this month. For now, Woodson said he would like to be a head coach again.

“I would be crazy not to,’’ said Woodson, who served six seasons in Atlanta. “I’m still under contract with the Clippers. Somebody calls me and gives me the opportunity to talk, I’d be happy to talk.’’