Mr Murray, who lives on Route Orange in St Brelade, has been at the helm of the north-east club for 20 years.
But former player Niall Quinn, with the backing of a consortium, is still in talks to take over the club.
Mr Murray (59) has admitted that he has been hoping to sell his stake for more than a year and has spent the last couple of months in talks with ex-striker Quinn and his business partners.
The Irish consortium are in the process of preparing a formal offer for his majority shareholding which, if accepted, would have to be extended to the other shareholders.