According to the description, the jetpack crashed in a lake in late 2016 so cannot be flown.
Canterbury Museum director Anthony Wright told the Herald Martin developed his first jetpacks in his Christchurch garage.
"So the Martin jetpack story is a fantastic tale of Canterbury innovation in the mold of Richard Pearse's aircraft, Bill Hamilton's jetboats and John Britten's motorbikes.
"We want to acquire a jetpack to make sure we're able to tell that story in the future," he said.
Wright said the jetpack itself is visually pretty amazing and they imagine it would be a hit with younger visitors in particular.
"It might even inspire future inventors."
There appears to be a lot of interest in the jetpack, with a total of 112 bids made at 2pm on Monday.
Canterbury Museum was leading the way but has since been overtaken by one bidder.
Bidding on objects at auction is part of the job for the museum's curators, but it is always a nerve-wracking process, Wright said.
"Especially for high-profile objects like this one. We really hope we're able to bring this jetpack home for everyone to enjoy."
A Givealittle page was started by former Wayfare Group chief executive Richard Lauder in collaboration with the museum to raise money for the purchase.
"As an early investor and former director and chief executive of Martin Aircraft Ltd, I'm keen to keep a jetpack in Canterbury," Lauder said on the page.
The jetpack, model P12 ZK-JMK, was powered by a custom-made 200hp V4 two-stroke petrol engine based on the Honda CR500.
The frame was mostly constructed using Carbon Fibre and it has a digital display.