Money from the sale would be shared between them and Mr Gay's other siblings.
"He was sick for quite a long time with cancer, and he was young, he was only 29 when he passed. He wanted to give them something if that sold," Mr Olsen said. "He and a friend of his went up to the concert. They actually had a fight over it and didn't talk for six months because she thought she caught it.
"He ended up with it anyway, and it sort of got passed on to me. And I've got no use for it really, it's just a hat to me."
As of yesterday there were no bids. The auction closes on Wednesday.
Photos of the slightly curled black hat and a ticket to the Auckland concert are provided.
Potential bidders are directed to a YouTube video of the 1996 show where Mr Olsen said Danny could be seen grabbing the hat at the end of the song Billy Jean.
Although some would question whether the hat was genuine, Mr Olsen said experts could easily confirm its authenticity. He said he has previously sent photos to an auction house in the United States who confirmed they were of a type of hat that would have belonged to Jackson.
People on Trade Me have so far suggested Mr Olsen try to sell it on eBay or reduce the price.
One suggested he cut it into pieces: "I would be interested in one square inch for, say, $20."
But Mr Olsen said he was confident the hat was worth $45,000 - especially since Jackson's death.
"I actually put it on [Trade Me] before Michael Jackson died. And I got up to $23,000 offered for it. But I thought, nah, I think it's worth a bit more than that."
