The club hold a buy-back option of around £13m on the stadium and £5m on Thorp Arch.
Leeds chief executive Shaun Harvey said in the Yorkshire Evening Post: "We have approached the council with a request that they assist the club by providing a mortgage so we are able to re-purchase both the stadium and Thorp Arch.
"The mortgage sought from the council would be comfortably covered by security in the form of a charge over the stadium and Thorp Arch and also a personal guarantee from a prominent Leeds businessman."
Harvey concluded: "If the club owned the stadium then there would no longer be any mystery as to who owns Elland Road. It would enable the club to play a full part in the redevelopment of the Elland Road area and create income streams to support the club on days other than matchdays."