Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
Mumble, along-serving Safa staff member, was elevated after Robin Petersen was redeployed to head a newly established Safa Development Agency.
Safa bosses were still mum yesterday on the departure of Petersen and appointment of Mumble as the new head of administration.
But Sowetan can reveal that Mumble has already been approached for the job by Safa president Kirsten Nematandani and has accepted the challenge.
There were other top soccer bosses who spoke to Mumble prior to his meeting with Nematandani to influence him to accept the job.
Mumble could not be reached for comment, while Nematandani said Safa will speak on the matter at the appropriate time.
An impeccable source within the Safa executive committee, who is familiar with developments surrounding the CEO's position, has confirmed that Mumble has been given the nod.
"I can confirm that Robin is going to be redeployed and Dennis is coming on board as the new chief executive officer of Safa, finally.
"The process has been handled at the Safa presidency level and has been kept under wraps for some time now to avoid any leak.
"The general feeling is that Dennis has been part of the senior staff at Safa for a long time. He is familiar with the environment and politics.
"We can't keep on overlooking him every time the position of CEO is available," said the official, who spoke on condition of anonymity.
A senior Safa staff member has also come out in support of the appointment of Mumble.
"Dennis is a hands-on man who believes in teamwork."
Sowetan understands that Petersen has been working behind the scenes to establish the new entity to be launched today.