The museum wants the whale, but its deputy director of collections and research says the facility isn't sure it can afford the task of dismantling the massive beast in Rocky Harbour and transporting it to Ontario.
Mark Engstrom says the museum is looking for sources of funding, but isn't seeking any money from the tiny Newfoundland town of 1,000.
Crews from the museum have spent the last few days recovering another blue whale carcass near Woody Point, N.L.
Engstrom says crews had to arrange for a larger truck container to ship the whale's cranium after the first one ended up being too small, which has added to the rising costs of the retrieval process.
He wasn't sure how much money has been spent on the project so far.
Bones from the 23-metre female will be trucked to Trenton, Ont., where Research Casting International, which specializes in museum displays, will help further handle the remains.
It's believed the two carcasses are among nine blue whales that were crushed or drowned in unusually thick pack ice earlier this spring.