Herald Sport understands that efforts were made by the Ibrox club yesterday to contact Murray with a view to resolving matters after the directors asked him to step down during a board meeting last week.
Concerns had been raised about his personal conduct after complaints by fans, with the issue brought up in the two board meetings prior to last week's. Any announcement about Murray's position would need to be made to the stock market first, with Rangers listed on the Alternative Investment Market.
If Murray steps down, the club could, in theory, appoint an interim non-executive director, rather than continue without a recognised chairman. There are four non- executive directors at Ibrox, with Scottish businessman Ian Hart, Philip Cartmell and Bryan Smart all contenders for the role if Rangers did decide to go down that route. Walter Smith, the fourth non-executive director, has previously emphasised that he has no interest in such a position, at any time.
No discussions have been held about decisions that would need to be taken if and when Murray steps down. The directors are able to make appointments without shareholder approval until the annual general meeting, and in turn could sack Murray, although there is reluctance to take this course of action.
Rangers also yesterday reached an agreement with Rapid Vienna over the debt on the fee owed for Nikica Jelavic. The Ibrox side have now had a payment of £717,000 accepted by the Austrian club. However, that is still believed to be around £286,000 short on the original £4m sum agreed between the two when the Croatian striker moved to Glasgow in August 2010. That money is owed by Rangers Football Club plc, which is currently being liquidated.
"We received the money from 'new' Rangers on Tuesday and the matter with them is closed," a spokesman for Rapid Vienna said. "We have assured them we will not raise any debate with FIFA which could have potentially blocked their participation in future European competitions. We are still trying to recover the full amount from the 'old' Rangers, but we understand that may take many months."