Auction Avenue director Kaleb Willems said the bidder was South African.
"The auction was well attended with a buzz surrounding the sale of the island," Mr Willems said.
"All we can say at the moment is that it’s a South African bidder. The prominent South Africans that are planning to put in offers have asked that their names be kept confidential until the offer has been accepted."
The auction of the 17ha island in the archipelago between Greece and Italy has been hailed as an uncommon offering in the local auction market.
The island belonged to a Greek family based in South Africa, and was held in the family’s trust.
The vacant island is zoned to accommodate up to six houses. Mr Willems said the nearest airport was "about two hours" away by boat.
The neighbouring island, less than 1km away, was owned by the Qatari royals, Mr Willems said.

