Snell isn't sure how he came to part with his singlet.
He always suspected it was left behind when he and his family emigrated to the States in the early 1970s.
But he now thinks it might've been donated for a charity auction.
"It's probably something that I might've kept," he said.
The unique piece of sporting memorabilia is stitched with Snell's racing number '466' in black on white below an embroidered 'New Zealand' and trademark 'Silver Fern'.
The manufacturer's label which is overstitched with Snell's name tag, 'Snell, P.G.', shows some signs of "age, minor staining and deterioration".
The vendor, who wishes to remain anonymous, is a 67-year-old Aucklander who says the jersey was gifted to his family "in the not too distant past".
It has been authenticated by a "very well known New Zealand sportsman" who was also at the Tokyo Games, he says.
The seller, himself was a top schoolboy runner, suffered a severe spinal injury nine years ago.
He told the Herald today that he wants to use some of the proceeds to undergo stem cell therapy trials in the US.
"I got it nicely framed up and had it in my home for quite a long time. I don't really want to see it go out of this country," he said.
Snell, who holds a PhD in physiology and is a much-sought after world expert on exercise physiology, would prefer it ended up somewhere like the New Zealand Sports Hall of Fame in Dunedin.
The Hall of Fame already houses one of Snell's 1964 Games gold medals.
And he plans to let them have the other two golds, he told the Herald today.
"I think they'd be better there than necessarily staying within the family. I've been there [to the museum] and I think they've done a good job," he said.
Hall of Fame chief executive Ron Palenski said it would be "fantastic" to be gifted the medals.
"Our reason for being is so that New Zealanders can see what these guys won and what they did," Mr Palenski said.
He said the black singlet has a value "way beyond money".
"I would hate to see some rich person take it beyond the reach and sight of ordinary New Zealanders."
Te Papa refused to say whether it had an interest in any such auctions, as it's "possible that this could affect price and bidding".
Snell is widely considered one of the greatest middle-distance runners of all time, and noted as New Zealand's athlete of the 20th century.
By the time of the 1964 Olympic Games, Snell - a protege of legendary Kiwi athletics coach Arthur Lydiard - was already a world record holder and 800m gold medal winner at the Rome Olympics in 1960.
In Tokyo, he defended his 800m title before also claiming gold in the 1500m.
Today, he looked back fondly on his career, especially New Zealand sport's 'Golden Hour' when he won the 800m final at Rome, and half an hour later, his mate Murray Halberg won the 5000m race.
"When Murray and I pulled off successive events, back to back, that was pretty nice. We really felt we'd done something significant. That was the most memorable thing in my life," he said.
"It's very nice to be remembered fondly, for sure. I look back on it with a degree of pride, but one has to move on and do something else with your life, and I've tried to do that. But this always comes back as a very pleasant memory."
