Western Isles Council has suggested the golden eagle and white-tailed sea eagle should be placed on a proposed list of species requiring careful management.
The white-tailed sea eagle was reintroduced to the west coast
The authority believes there is a clash between efforts to protect the birds of prey and the needs of islanders.
This view will be included in the council's response to Scottish Natural Heritage's (SNH) consultation on a Species Framework.
Eagles have been blamed in recent weeks of preying on crofters' lambs.
The birds, which live almost exclusively in the remotest areas of the Highlands and Islands, have also had an impact on a proposal to build a wind farm on the Eishken Estate on Lewis.
Estate owner Nick Oppenheim, the man behind Beinn Mhor Power, has drawn up a revised £120m plan for 53 turbines instead of the 130 originally approved by Western Isles Council.
The Royal Society for the Protection of Birds (RSPB) Scotland had raised concerns about the effect of the proposal on the raptors.
SNH is in the midst of a public consultation exercise on a Species Framework which will set out how Scotland improves natural habitats and protects and manages species.
The council has backed the main principles put forward by the conservation body.
However, the council's sustainable development committee chairman, Archie Campbell, has warned that there was an issue about golden eagles and sea eagles taking lambs.
White-tailed sea eagles are the UK's largest bird, followed by the golden eagle, and had to reintroduced having been wiped out in the 19th century.
Populations of the bird are confined to west coast of Scotland.