The row follows the sale to Ms Gloag of Manston Airport, in Kent, for just £1 last year. Since then she has announced plans for it to shut, with the loss of mostly part-time jobs.
Earlier this month it was reported that the airport had rejected an offer to buy it from an American firm.
Yesterday local MP Roger Gale asked for the Prime Minister to intervene during Prime Minister's Questions.
In response, the Prime Minister said: "Ultimately, the future of Manston remains the responsibility of the airport owner, but it is important that the Government are engaged."
He said Transport Secretary Patrick McLoughlin will speak to Mrs Gloag.