Last week, Sefton Council rejected an application to let them stay for another four months on health and safety grounds.
But Another Place Ltd, the organisation set up to raise £2m to buy the artwork to keep it on Merseyside, say the concerns can be addressed.
The trust is currently working with council planning officers and consultants to see how best to delay the scheduled removal date on October 31. It will then decide whether to appeal against the council's decision, which could result in a public inquiry, or submit a fresh application to retain the statues permanently.
The campaign has seen a groundswell of support and a petition of Merseyside residents has already been signed by 1,500 people.
Crosby MP Claire Curtis-Thomas and Another Place creator Antony Gormley have backed the campaign, as well as a host of business and tourist leaders.
Following the council's decision, local authorities across the region have expressed an interest in playing host to the army of iron men, including Lancashire County Council and Wirral Borough Council.
Liverpool leader Warren Bradley has also come out in support of the campaign.
Since they were installed in Crosby last year, they have been visited by more than 600,000 people and are expected to boost the local economy by up to £10m over a decade. ¦ WHAT do you think?
Should the Gormley statues stay or should they be moved to Another Place. Log on to liverpooldailypost. co.uk to register your vote.
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