Speculation has abounded in recent months with regards potential investors but, asked if there had been any expressions of interest, Murray told The Scotsman: "No - none," adding that there was "no substance" to such talk.
He also dismissed rumours that Lloyds Bank was effectively running the club, saying: "We are hoping to go into break-even and make a small profit.
"It's not going to be a lot, but there will be no further losses.
"I've made it quite clear that with the banking facility the club would have to work within its financial means.
"When the speculation got mischievous was when people started talking about mysterious Florida millionaires.
"It was unbelievable."
Murray continued: "For the record, I will repeat that I am totally prepared to sell the club.
"Price is important but it is not the most important factor, as long as you hand it over in the best interests of the football club.
"Before I stepped down I made it clear we will not sell any of our prime assets while we are fighting for the league.
"Rangers is no different from any other business. Lloyds has given us a facility and we are no different from a household or a business. The club must work within that.
"If people don't like that, well, they are not living in the real world.
"I think you will find that every other football club has gone the same way."
Reports that Lloyds are running the club have particularly irked Murray.
Parent group Murray International Holdings' new man on the Rangers board is company turnaround specialist Donald Muir. Murray insists the 50-year-old accountant is paid by him, not Lloyds Bank.
"I approached Donald in June. I thought he had skills we didn't have. Donald was a pal of (former boss) Alex McLeish, so we knew him through football," he said.
"He's helping me with change. He'll help to teach an old dog new tricks."
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