RSPB Scotland said it was "not in a position" to buy Ailsa Craig at its £2.5 million asking price.
The island, which lies 10 miles west of Girvan, is home to tens of thousands of seabirds and is currently leased by the conservation charity and managed as a nature reserve.
The charity said it was looking into the prospect of taking ownership of Ailsa Craig when it was revealed it had been put up for sale by Charles Kennedy, the eighth Marquess of Ailsa.
Known as "Paddy's Milestone", the Craig is home to 70,000 birds, including gannets, guillemots and herring gulls as well as the special granite used for Olympic gold medal winning curling stones.
Dr Dave Beaumont, RSPB Scotland regional reserves manager, said: "We are very proud to be the leaseholder of such an important landmark as Ailsa Craig.
"There have been rumours that the RSPB is in discussions to purchase the island, but this is not the case.
"Because of its international importance as a seabird colony, we have a definite interest in its future, but we are not in a position to buy the island at its current asking price.
"We rely on the generosity of individuals and grants from public and commercial bodies for our income, and as a charity we need to make sure these funds go as far as they can.
"Our lease on the island runs until 2050, and this currently allows us to achieve our conservation goals.
"We will be watching the sale closely and will be very keen to work with the new owners to further the conservation of this magnificent island."
The island is about two miles wide and rises 1100 feet above the sea.
The new owner will be able to look forward to rental income of about £26,000 a year.
The company that makes curling stones has a lease to extract the famous "blue hone" granite from a quarry on the island.