The cost of keeping the famed black swans of Dawlish in their natural habitat is expected to reach thousands of pounds.
Dawlish Water in Devon has silted up so much that only five of the birds remain, out of 15 which were originally brought over from Australia.
Teignbridge District Council and the Environment Agency are meeting next week to discuss what can be done.
But "a good reason" is needed to spend money on major work, the council said.
The swans have been a major tourist attraction for decades and are used as the town's emblem.
They were brought to Dawlish, from Australia, at the start of the 20th Century.
But now the water course is filling up with silt and recent attacks by dogs have forced the birds them to move elsewhere.
A spokeswoman for landowners Teignbridge District Council said: "De-silting is a very costly exercise and we always have to ensure there is good reason to spend taxpayers money on major work."
She said the council recognised concern about the future of the swans and had scheduled a meeting with the Environment Agency and the Town Council.