The move follows the preferred bidder for the South Ayrshire site withdrawing last week because of uncertainties caused by the Covid crisis.
Its identity has never been confirmed, but The Scotsman has revealed it was AGS Airports, which owns Aberdeen, Glasgow and Southampton.
Mr Matheson declined to say how many parties had expressed interest in buying the airport but said it was more than one.
No sale to military
He told the Scottish Parliament’s connectivity committee the bidder’s decision “means Prestwick can engage with other interested parties.
"That engagement is underway.
"It presents an opportunity to re-engage with other interested parties and new ones.”
However, the minister said the airport would not be sold to the military, or for non-aviation uses such as housing or business development.
But he would not confirm that Scottish Government loans to keep the airport open which now total £43.4 million would be repaid as part of any sale.
These have been provided since ministers bought the loss-making airport in 2013 for a nominal £1 to avert its threatened closure.
‘Very important sector’
Mr Matheson stressed the importance of Prestwick as a “significant employer”, with around 300 jobs on the site and some 1,000 among nearby aerospace businesses which depend on it.
He said: “It is important to recognise that that investment by the Scottish Government in Prestwick not only sustains the airport but also helps to sustain a very important sector.”
Mr Matheson said the airport had not started to repay the loans and might need to use part of the £3m profit made in 2019-20 because of the downturn caused by the coronavirus pandemic.
‘Remain as an aviation facility’
However, he added: “We will take an approach that will be in the best interest of the taxpayer in Scotland.
On future use of the airport, he said: "There are no plans to sell the airport to the military.
"The sales criteria made it very clear it would remain as an aviation facility.”
Mr Matheson said the sale had been paused at the request of the preferred bidder, who had been selected late last year.
The minister expressed surprise when a Conservative member of the committee asked why there had not been job cuts at Prestwick during the Covid downturn like at privately-owned Scottish airports.
North east Scotland MSP Peter Chapman said: “You mentioned the 300 jobs at Prestwick airport.
"Unfortunately, we know that the privately-owned aviation industry is shedding jobs at a very rapid rate just now.
"Is this now happening at Prestwick?
"And if not, why not, because given the taxpayer will eventually pick up the tab for any losses.”
Mr Matheson said: “I’m not sure if that was a demand for us to have folk laid off at Prestwick, because if it is, it’s not the approach we want to try to take.
"I certainly don’t think we should get ourselves into a situation where we’re demanding that assets such as Prestwick are looking to start laying off staff unnecessarily.”