"The Labour politician, who was only elected in May, released a lengthy statement on the topic this afternoon following a series of meetings.
The airport's owners, Peel Group, announced this week that commercial aviation was no longer viable at the site and that they were reviewing the airport's future.
Mr Coppard hinted that buying the airport, as happened to Durham Tees Valley under Teesside's metro mayor Ben Houchen, was a possibility but not a favoured course of action.
The statement read: "A quick update on where we are with Doncaster Airport at the end of a pretty difficult week. Since finding out the news about the owners plans for the airport late on Tuesday, I’ve met with leaders of the four SY local authorities and most of our region’s MPs.
"Yesterday I wrote to the owners of the airport - Peel Group - to express my disappointment about their lack of ambition for DSA and their failure to communicate their plans sooner.
"While the announcement made by Peel is to ‘review’ the viability of the airport, my worry is that they will seek to shut down the site and then simply sit on the site, demanding planning permission to turn the airport into housing or retail.
"I want to see DSA thrive, and there is no reason an airport with great facilities and a catchment of millions shouldn’t be successful. While Heathrow and Manchester struggle with capacity, regional airports like ours should be able to pick up the slack. Levelling up, if you will.
"What needs to happen next? I will be meeting with the main board of Peel Group on Wednesday to discuss their approach and ask them some hard questions about their approach.
"I’ve already made it clear that I expect to be able to input into the terms of reference for their review. I will be asking them to explain their approach and why they chose not to engage with us prior to making their announcement last week.
"We also need the government to work with us respond to developments this week. They remain responsible for aviation and regional airports, and are supposed to have a plan.
"I realise there is a Tory leadership content going on but Grant Shapps has to get a grip on this, and make it clear to Peel they can’t cut and run. Nick Fletcher MP has said he will use his influence with govt to make that meeting happen. I’m grateful for his support.
"A couple of other points to make in response to some questions I’ve been asked since Tuesday. We were in discussions with Peel about a £20million loan, for investments in the airport. That loan would have been on top of the £8million already loaned to them by South Yorkshire.
"That loan had stalled after Peel refused to share the financial information we had asked for, as part of our due diligence and to make sure that money was safeguarded.
"However, they have already said that loan was not a material factor in their decision to review the viability of DSA.
"I’ve also been asked if we can buy the airport. We’re not ruling anything out, but the model for that is the approach taken in Tees Valley. All the evidence so far seems to indicate that’s a huge financial risk.
"The airport has continued to suffer the effects from the covid-19 pandemic while also carrying out major investment in the site.
"The best people to run an airport are people who know airports, airlines and aviation. The public sector has invested hugely in the DSA site and the private sector should now step up and match that ambition.
"Finally, I’ve been asked if we should be supportive of the airport in a climate emergency. I am utterly committed to our net zero goals. But sustainable aviation has to be part of our future.
"More people flying from DSA does not have to mean more people flying. Whoever owns the airport I will expect them to pursue an ambitious sustainability strategy as part of our wider clean growth agenda.
"South Yorkshire has world leading universities, working with companies pursuing innovation at the cutting edge of aerospace innovation. We can be both the solution and the beneficiary.
"I’ll keep on updating people about developments, but for now we’ll be working to explore any and all solutions, and pressing both Peel and the govt to act in the interests of our community."