Mumble saw his contract expire in September, with Russell Paul currently serving as interim CEO of the association.
SAFA president Danny Jordaan said the post will be advertised soon.
Asked why Mumble was not retained, Jordaan said: "The reality is that Denis Mumble has reached the stage where he can retire and the NEC said we should advertise the post."
Jordaan roped in Mumble's services when he became SAFA president in September 2013.
Mumble previously served as a team manager to Bafana Bafana in the lead-up and during the 2010 FIFA World Cup on home soil.