The 19th Century bones, believed to be those of a Greenland right whale, were recently gifted to North Sunderland Parish Council by Northumberland County Council.
They were in the grounds of the former first school until they went missing in December 2018, later found dumped near North Sunderland Football Club, and had been in storage until September.
A section of the whalebones remains in the ground at the former school and it is hoped a way could be found to piece them back together.
Cllr David Shiel, who has been studying the way Whitby’s famous whalebones are installed, said: "We need to see if we can get the top bits (encased in concrete at the old school). We can do nothing until we find out what length those pieces are.”
Chairman Geoffrey Stewart believes around four feet of the whalebone could still be in situ.
"That part of the land still belongs to the county council,” he added. “They will give us a price for digging them out.”
Meanwhile, concerns were raised about a planning application to construct a roof terrace in place of a pitched roof at a holiday let on Union Street, creating an additional bedroom.
The Northumberland Coast Area of Oustanding Natural Beauty and a number of local residents have also objected.
Cllr David Donaldson said: “There is already restricted parking in that yard and it’s extremely difficult to find a space on the street.”
Cllr Maureen Bramley added: “It’s not in keeping with the conservation area.”
Parish councillors also had issues with proposed changes to Juniper Cottage, South Street, including changing two windows to Juliet balconies.
“It’s out of keeping with the old quarter of Seahouses,” said Cllr Donaldson.
However, members were happy with a revised application for proposed works at The Dunes, St.Aidans.
"It looks much better,” said Cllr Donaldson.
Councillors were also happy with plans to replace the existing conservatory at The Olde Ship Inn to provide an indoor seating/viewing area within the beer garden.
A quote for just over £4,000 for works in the cemetery was also approved.