Brian Kennedy's revised verbal bid for Rangers has been rejected by administrators Duff & Phelps, a spokesman has said.
The Sale Sharks owner is one of three parties who are hoping to purchase the SPL club.
Kennedy claimed on Wednesday that he had made an "improved" offer for the former champions after a previous bid had also been turned down.
However, he has now been told that his latest offer is not "capable of acceptance".
Bids from American Bill Miller and a Singapore group headed by Bill Ng both remain in the frame after Paul Murray's Blue Knights Consortium withdrew from the process.
