"Leeds City Council must commit no time or money to any project with Leeds United until it is clear who the actual owners are," the MP argued.
"The issue also raises huge questions for the Football League, to ensure that football club owners are approved 'fit and proper people' according to the league's own regulations."
Burgon's comments followed the Guardian's revelation this week that according to a statement sworn in a Jersey Court by the club's chairman, Ken Bates, Leeds United is owned by unidentified holders of 10,000 shares in the Forward Sports Fund, registered in the Cayman Islands.
Bates had previously told the court he and his financial advisor, Patrick Murrin, owned one "management share" each in Forward.
That, Bates said subsequently, had been "incorrect" and "an error on my part".
The council has agreed in principle to borrow money, thought to be £6m, to buy Thorp Arch and lease it back to the club, who approached the council for financial help this summer.