The Scottish government has been seeking a buyer for the airport, which is 40 minutes south of Glasgow and said in February it was in talks with a preferred bidder. The unknown potential buyer emerged after a previous bidder pulled out due to the pandemic.
The BBC said ministers had decided against a sale “at this time”.
The attempt to bring the airport back into private ownership is now approaching its third year, with Prestwick having mainly served cargo flights during the pandemic.
The Scottish government paid £1 for the airport in 2013 when it was threatened with closure after owners Infratil sought to offload it. Ministers said the airport had made an operating profit in 2020/21.