The 15th Century ship was uncovered in the banks of the River Usk during construction work on a new arts and theatre complex for Wales' newest city.
A £3.5m Welsh Assembly Government grant to preserve the craft was pledged in August after a high-profile campaign mounted by archaeologists.
But it has emerged that cash refers only to restoration of the main hull.
Newport councillors meet on Thursday to examine whether the money will extend to the rest of the ship.
Activists believe the ship to be of national significance and older than the Tudor ship, Mary Rose.
Thousands of people flocked to the bank of the Usk during the summer as contractors made way for archaeologists' attempts to lift the boat.
Many locals have found an affinity with Newport's new discovery at a time when the city is finding its feet as Wales' third metropolis.
The bow and the stern are still buried at the site.
Museum ship
Timbers are being stored in water tanks at Corus' nearby Llanwern steelworks - preventing erosion by air - until a decision on their eventual fate is made.
The remains of the ship will be displayed at their planned resting place in Newport's new arts centre, scheduled for a 2004 opening.
Visitors will be able to see it through a glass floor, and there will also be a viewing gallery on the lower level.
But unless councillors can find a way to raise yet more money, the prized relic could be without its bow and stern.
The value ascribed by historians to the vessel could then be lost forever.