Fox has opted to stay with the entertainment retailer, telling the HMV board that he remained committed to driving its turnaround strategy which is due to go into its third and final year.
He had been widely tipped to take over ITV executive chairman Michael Grade’s role as chief executive.
External frontrunners now include Pascal Cagni head of Apple Computer in Europe and former BSkyB chief executive Tony Ball.
The latter is again considered a strong contender, despite previously falling out of favour with the ITV board when he decided to join BT as a non-executive director.
Other contenders include Guillaume de Posch former CEO and chairman of ProSiebenSat.1 and ITV chief operating officer John Cresswell.
Last week ITV reported a pre-tax loss of £105m in the first half of the year, while net ad revenue fell 15%.