Sir David Murray claims Rangers can attract willing investors if the club is run in an efficient manner. Murray this week announced he was no longer "actively marketing" his controlling stake in the club after failing to secure an offer in the "best interests of the club, its shareholders and fans".
Murray had declared himself open to offers in October 2009, more than a year after the club suffered a sudden downturn in financial fortunes.
The failure to secure a suitable deal for ownership of the back-to-back Clydesdale Bank Premier League champions has prompted fears from some fans over the club's long-term future.
Murray said in the Evening Times: "The answer to that is it will be if it is run efficiently in a cost-effective manner - that is the way it will survive and be attractive to someone."
Murray added that there had been "major improvements" in his business interests since the club's fortunes fell away following their Champions League qualifying defeat by Kaunas in August 2008, which was quickly followed by the global economic crisis.
"At that time our bank went out of business, the price of commercial property collapsed, the football club had just lost to Kaunas, and the price of metal collapsed," said Murray.
"We have a working relationship with Lloyds, who didn't know us a year ago and are backing many of our ventures, some in the pipeline. There is stability in our business."