The offer was withdrawn after its bid for the Ibrox club passed a midday deadline for a decision from administrators Duff and Phelps.
Brian Kennedy, owner of Sale Sharks Rugby Club, had become involved in the attempt to takeover Rangers after the collapse of the preferred bid from American Bill Miller. But Kennedy had warned they must accept the Blue Knights' offer for the club by noon on Friday, or else they would walk away.
Earlier Kennedy told the Daily Record newspaper they were now at the "end of the road.
"If our bid is not accepted in the next few hours then, most reluctantly, we will have to withdraw from the process by lunchtime," he had said.
"We have a plan to save this club but my lawyers, Walker Morris, have advised me it will not be possible to execute a CVA unless, on Saturday morning, we begin working, full-time and flat out on due diligence and documentation.
"Any later than that and our plan cannot be delivered with any legal certainty.
According to Duff and Phelps, three potential ownership groups emerged in the wake of Miller's withdrawal to rival the Blue Knights.
Duff and Phelps confirmed that the Blue Knights, which was previously led by former director Paul Murray, has pulled out of the race after they did not receive an acceptance of their offer by Friday's noon deadline.
Earlier on Friday it was announced that Rangers' appeal against a fine and transfer embargo would be held next Wednesday.
