The Glasgow club are £31m in debt and under pressure from Lloyds Banking Group to control costs.
Rangers say the talks with Ellis are at an early stage, but Murray, who stepped down as chairman of the club last August, has set up an independent committee of the board, including playing legend John Greig, to consider any interest.
Ellis, a former director at Queen’s Park Rangers and chairman of Northampton, is at the forefront of London-based consortium, RFC Holdings (Guernsey), who have approached Murray with an estimated £33m offer.
But he faces competition from an Asian-based group and interest from a third party headed by South African exile Dave King, who has previous links with the club.
Confirming the talks, a club statement read: “The board of RFC understands that discussions are at an early stage and there can be no certainty that any offer will be made for the issued shares of RFC.”