Ellis has previously apologised for the delay in a takeover being agreed
The Andrew Ellis-led consortium is in "advanced negotiations" with Rangers to buy a controlling interest in the club.
Ellis and his company, RFC Holdings, informed the Stock Exchange on Wednesday that talks were at an advanced stage.
The consortium first registered its interest in the club in March.
Speaking last month, former Northampton Town owner Ellis apologised to the club's supporters over the length of time it was taking to strike a deal.
Ellis's consortium is considering a reported £33m bid for the Scottish champions, who are about £30m in debt and who have admitted that they are being investigated by HM Revenue and Customs, with reports claiming the club faces a £24m tax bill.
Rangers chairman Alastair Johnston has previously criticised Ellis for the delay in preparing his proposal.
And on Wednesday, a statement on the Stock Exchange read: "The company confirms that it is in advanced negotiations with Sir David Murray to acquire a controlling interest in Rangers Football Club plc.
"However, no price has been agreed and no timing has been established for the conclusion of the talks.
"If a deal is concluded between Sir David Murray and RFC, the company would be required under Rule 9 of the City Code on Takeovers and Mergers immediately to make an offer for the remaining issued share capital of Rangers.
"It is emphasised that this announcement does not amount to a firm intention to make an offer and there is no certainty that any offer will be forthcoming, or as to the terms of such an offer."
Sir David Murray, who relinquished his chairmanship and place on the board in August, controls about 90% of the shares in Rangers.
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