The airport has been local authority-owned since 1987
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Leeds City Council is planning to sell its 40% interest in Leeds Bradford Airport to the private sector.
The airport has four other shareholders - Calderdale, Bradford, Kirklees and Wakefield Councils - who will meet soon to discuss their responses.
Leeds Councillor Andrew Carter said there were development constraints as the airport was publicly owned.
"The airport business is complex and we believe this sort of commercial risk is more suited to the private sector."
He added: "Presuming the disposal goes ahead we will be asking for safeguards as regards the airport's future.
"We also understand the public's concerns regarding the council's position as a planning authority for a major commercial enterprise in which the council is a shareholder."
Leeds Bradford International Airport was originally Yeadon Aerodrome, which began operating in October 1931. The five local authorities took over its ownership in 1987.
The airport currently serves 60 direct destinations and was used by more than 2.5 million passengers in 2005.