The heavily indebted hub was put up for sale by the Scottish Government in June, six years after buying it for a token £1 to avert closure.
The sale documents indicated that a preferred bidder for the airport was expected to be selected in the first week of September with the sale completed by about 4 October.
However, there has yet to be any announcement of a preferred bidder, or confirmation that a sale is imminent.
It comes as the airport is at the centre of an investigation by the House Oversight and Reform Committee in the US Congress which includes US Defence Department payments and patronage at the state-owned airport.
Now, amid ongoing doubts over the negotiations with private parties, Michael Matheson has informed the convenor of Hiolyrood's rural economy and connectivity committee that the sale may fall through.
In his correspondence to Tory MSP Edward Mountain providing an update on the sale process, Mr Matheson wrote: "While efforts are currently focussed on returning the airport to the private sector, which has been our intention since purchasing the airport in 2013, should this not be achievable for any reason we will consider options for taking the airport forward in the future."
It is unclear what options the Scottish Government would look at if it is unable to sell Prestwick, which is reliant on loans totalling £38.4m from Scottish ministers.
Those in charge of the airport have come under increased scrutiny in recent months. As revealed by The Scotsman in October, multiple senior sources familiar with the airport’s business allege it is waiving service fees for inbound US Armed Forces aircraft at a cost to taxpayers of “seven figures" in order to bolster traffic and safeguard its commercial relationship with the US Defence Department.
Justice minister Humza Yousaf was alerted to the allegations last year while serving as transport minister, correspondence obtained by this newspaper shows. The airport has refused to respond to a series of enquiries about the allegations.
Mr Matheson's letter, sent on 16 November, did not expand on the progress of any sales discussions, noting only that the airport's senior management team is continuing to "consider the bids that were received."
It goes on: "As I am sure you will appreciate, consideration of bids and the work associated with the process are complex matters that require detailed assessment (both by Prestwick and by bidders), and ongoing discussions with interested parties.
"Good progress continues to be made and we are satisfied with how the sale process is developing."
Mr Matheson states in his letter that he remains committed to providing an update to parliament once he is "in a positionto do so."
He adds: "In the meantime, it is essential that we avoid any comment or speculation that could impact on the process."