Long term cash to help preserve the medieval ship found in mud in the river Usk needs to be secured, Newport Council has warned.
The ship was probably owned by the Earl of Warwick, known as The Kingmaker
Hundreds of timbers from the ship are being kept in clean water in special tanks at a warehouse in the city, with a multi-national of experts working on them.
But the council said it might have problems in finding the £300,000 needed each year, as part of the long-term
Council leaders have indicated that they wanted to start talks with the assembly government and would consider every option.
It could be 10 years before the ship is ready for display at a gallery in the Riverfront arts centre.
The 15th Century remains were uncovered by builders, during excavation work for the £16m centre in 2002.
Archaeologists believe the find could be more significant than the discovery of the Tudor ship, the Mary Rose.
The council said the project for this year was being funded from what remains of a £2.9m Welsh Assembly Government grant. A council spokesman said that the grant had already funded a "significant part" of the work which has included archaeology, building the Riverfront gallery and removing and storing timbers.
"However there are on-going costs for recording and restoration work which will be at least £300,000 a year for several years to come," he added.
The timbers of the vessel are being stored at a warehouse in Newport
Charles Ferris, of Friends of the Newport Ship, said there needed to be a wider focus on the "international importance" of the ship, with a look beyond Newport - and even Wales - for funding.
"It's like being given the Mona Lisa and saying we can't afford to do anything with it.
"At £300,000 a year, that's £3m over the decade - but they've just agreed to £12m to preserve the Cutty Sark."
The local authority said it hoped to obtain up to 70% of the funding it needed from outside Newport.