InstaPlant, which uses computer technology to fashion intricate displays, said the bedding would be great for parks, roundabouts and open spaces celebrating the games.
"The only problem is the organisers are not even allowing Olympic venues to use the rings logo and trademarks," said manager Chris Harnett. "Even such words as 'Olympic' and 'London 2012' are restricted in their use," he added.
So Harnett threw down his promotional challenge: "We will give away the two displays to any organisation that can win permission to display them."
He declared that if the London Organising Committee of the Olympic & Paralympic Games (LOCOG) refused permission, the displays "will be left here to rot and that would be a shame".
An Olympic spokesman said unlike the public Olympic Delivery Authority, which is building the venues, LOCOG was private and needed to make £2bn to stage the games.
"If Harnett wants to use the displays he can approach us to be an official partner, but there is no one-size-fits-all on cost. It depends on the product," he said. Non-profit groups were not barred from using the logo, he added, but circumstances had to be cleared with the organiser.