Kennedy confirmed reports that he submitted a £5.6million offer for a 51% shareholding in the Ibrox club on June 25.
Although the offer was not accepted, it appears to remain on the table.
The Scottish businessman failed to buy Rangers with both a solo bid and a joint offer with the Blue Knights consortium before administrators signed an exclusive deal with Charles Green's Sevco Scotland.
In a statement, Kennedy said on Monday: "I have recently had several confidential meetings with a gentleman representing the shareholders of Sevco, with regards to my interest in purchasing a majority shareholding in Rangers Football Club.
"The details of these meetings and the written offer I have submitted have been disclosed from within the club.
"Now that this has leaked I have I have no alternative but to confirm that what is reported in the Daily Record regarding such matters is accurate.
"I have no further comment to make at this time."
Sevco bought the assets of Rangers for £5.5million when the club was consigned to liquidation last month but doubts have continued over their funding after the newco club was consigned to the Irn-Bru Third Division, subject to ongoing talks over membership of the Scottish Football Association.
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