The revelation follows transport secretary Michael Matheson telling MSPs today that an undisclosed "preferred bidder" had been chosen.
He said its identity was not being revealed yet "to protect the integrity of the process".
AGS Airports, when asked by The Scotsman whether it was the preferred bidder, refused to comment.
A spokesperson for the group, which also owns Aberdeen and Southampton airports, said: “We have always stated we would welcome an outcome which returns Prestwick Airport to a commercial footing in the private sector.
"We have been monitoring the situation closely following the Government’s decision to place the airport on the market and will continue to watch with interest.”
It is not known whether £40 million in Scottish Government loans to the airport will be repaid as part of the sale.
The news follows the loss-making South Ayrshire airport being officially put up for sale in June, after ministers had bought it for £1 in 2013 to avert closure.
Mr Matheson told MSPs: "We made clear in 2013 that the Scottish Government intended to return Prestwick Airport to the private sector when the time was right.
"We were pleased the opportunity to buy the business, set out in the Official Journal of the European Union, attracted considerable interest.
"Following careful consideration of the bids received, I have accepted a recommendation made by TS Prestwick HoldCo [which runs the airport on behalf of ministers] to appoint a preferred bidder.
"To protect the integrity of the process I am not able to disclose the identity of the bidder at this time but we remain satisfied that good progress is being made in the interests of the business.
"I will update Parliament further in due course."
South Scotland MSP and Scottish Labour transport spokesperson Colin Smyth said: “The [Scottish] Government talks about protecting the integrity of the process, but the decision to sneak this news out on the last day of Parliament, with no opportunity for scrutiny by MSPs, brings that whole process into disrepute.
"We were told that any sale would be agreed by October.
"Two months later we are told the Government have effectively accepted a bid but they will keep the details secret and won’t provide a timetable for the completion of any sale.
"There are over 300 direct jobs and thousands more indirect [jobs] at Prestwick, so this will be an anxious time for the Ayrshire community who are being left in the dark.
"There is no reason whatsoever why the Government cannot answer the basic questions of whether this proposed sale guarantees to secure and grow jobs at Prestwick and whether there is agreement with the preferred bidder that the almost £40 million loaned to Prestwick airport will be paid back in full by them if the sale is completed."
Scottish Conservatives transport spokesman Jamie Greene said: “If there is positive news about a potential buyer for Prestwick Airport then that process should be allowed to take course and progress.
“But the Scottish Conservatives have been clear since the airport was nationalised, a significant amount of taxpayers money has been loaned, not gifted, to this business and we fully expect that any deal which comes to fruition will seek to recover those monies.
“The SNP has a notable track record of writing off loans and bungled contracts and sales of publicly-owned assets.
"For everyone’s sake, let’s all hope this isn’t another example of such."
Cunninghame North SNP MSP Kenneth Gibson, who asked the Scottish Government-initiated question, said: “I am delighted there has been solid progess in returning Prestwick to the private sector and look forward to further details being made public early in the New Year.
“Having saved Prestwick Airport from certain closure and the jobs connected both directly and indirectly, the Scottish Government and its agencies have worked hard to turn it around as a going concern.
"This can only be good news for Ayrshire and Scotland.”
Several bids were received by the September deadline, with the sale scheduled to have been completed in October.
However, Mr Matheson later told MSPs the process had taken longer than expected.
The airport announced last week its annual losses had halved from £7.6 million to £3.8m in the year to March.
Revenue increased by one third from £18m to £25m.
However, it owes the Scottish Government £40m in loans provided to keep the airport operating.
Prestwick has a sole passenger airline - Ryanair - which has reduced flights.
However, it has increased business from refuelling US and other military aircraft, and cargo operations.