Mr Fletcher, speaking to the Local Democracy Reporting Service at DSA, said Peel chairman John Whittaker ‘holds all the cards’ and ‘could make the airport a success.
But the Conservative MP said he ‘doesn’t think he is doing that’ at the moment.
Peel Group and DSA have both been contacted for comment.
Discussions between politicians, council officers, the airport and Peel have been ongoing since the shock announcement the site could close on July 13. There are around four weeks left of a ‘strategic review’ phase.
The review follows ‘lengthy deliberations’ by the board of DSA which has ‘reluctantly concluded’ that aviation activity on the site ‘may no longer be commercially viable’.
Airport bosses blamed Covid-19 and the recent departure of Wizz Air who moved their base operations from Doncaster. Their flights continue to set off and land at DSA.
On his visit to DSA, Mr Fletcher took a flight over the airport with the Yorkshire Aero Club, a flying school which trains budding pilots of the future.
Mr Fletcher also revealed that two more MPs have backed a campaign to save the airport from closure.
Conservative MPs Lia Nici, who represents Great Grimsby and Mark Eastwood, the MP for Dewsbury, have both thrown their weight behind the cause.
Mr Fletcher said: “I’ve spoken to the chief executive of Doncaster Council, I’ve been in communication with (South Yorkshire mayor) Oliver Coppard and I’ve written to John Whittaker at Peel, who is the main person we need to get round the table.
“He can decide not to sell Doncaster Sheffield Airport, he can decide if he wants to keep it open. It’s he who needs to be around the table and we need him to speak to Oliver Coppard to come to some kind of agreement to make sure there is a future for Doncaster Sheffield Airport.
“It’s okay putting your chief executive in the discussions but he is the chairman, he’s the man who holds all the cards, he could do all he can to make the airport a success.
“At this moment in time, I don’t think he’s doing that.”