They have launched an “emergency call to action” to prevent the 143-year vessel from being scuttled or broken up over fears a hurricane could see her sink in the harbour.
The desperate appeal follows a series of unsuccessful attempts to return the Falls of Clyde to Scotland for restoration.
She is the only four-masted ship of her type in the world and the last remaining of eight such iron-clad cargo vessels built on the Clyde..
The Save the Falls of Clyde and Friends of the Falls of Clyde groups said: “The Hawaii Department of Transportation, Harbours Division, has posted a request for disposal with a drop-down date of May 21.
"Once she is scuttled, this iconic piece of our maritime heritage is lost forever from future generations.
"We are in desperate need of your support, by speaking out and with financial contributions.
"We need to get the ship lifted to the River Clyde where she will be restored.
"Our proposal for the salvage and repatriation of the Falls of Clyde will be the most effective method from an environmental, harbour safety, and financial standpoint.
“We will use a submersible lift ship to float the Falls of Clyde on to their deck and then lash her down for the voyage back to Port Glasgow.
"She will be rebuilt as a fully rigged sailing ship once again.
"She will also offer education at sea, with opportunities for students to learn how to sail a tall ship and hands-on education on the climate and marine environment.
"We must prevent this substantial part of Hawaii’s and Scotland’s heritage from being discarded by deliberately sinking her at sea.”
Save Falls of Clyde – International director David O’Neill added: “Two major offshore engineering, salvage and shipbroker companies are helping us put together a professional proposal to manage this operation, not only to the satisfaction of the Hawaii authorities but also to Peel Ports, from whom we are asking for permission to bring her into the Clyde.”
Falls of Clyde was built by Russell & Co in Port Glasgow as part of the Falls Line fleet, named after Scottish waterfalls.
The 266ft (81m) vessel has spent most of her life in the US, initially transporting sugar from Hawaii to California.
She later became a tanker under owners such as oil firms Chevron, Marathon, BP and Exxon.
The US Navy helped rescue the ship by towing her from Seattle to Honolulu, in 1963, where she has remained since.
The ship was opened to the public in 1971, but she suffered severe damage in a hurricane in 1982.
The Hawaii Department of Transportation is seeking bids for the “removal of the derelict sailing vessel Falls of Clyde from Honolulu harbour”.
Harbours Division deputy director Derek Chow said the Friends of the Falls of Clyde had pledged to remove the vessel more than a decade ago, and had been moored illegally since 2016.
He said: “The time for the Friends to try to prevent the removal of its vessel from the harbour has passed.”
Mr Chow told the Star-Advertiser newspaper in Honolulu that the vessel was at risk of sinking in a hurricane, and hoped it could be moved before the start of the hurricane season next month.