The Ahly coach has rejected the offer from the South Africa Football Association (SAFA) and is determined to see out his two-year contract with the Egyptian giants.
The 56-year-old says he's committed to the Red Devils and does not seek a second stint with the Bafana Bafana.
Portuguese coach Carlos Queiroz has also turned down the chance to return to the team with SAFA turning its attention to Mosimane.
However, the rejection of Mosimane, means SAFA is desperate to find Molefi Ntseki's replacement ahead of the 2022 FIFA World Cup qualifiers.
Herve Renard, Hugo Broos, and fan favourite Benni McCarthy are also being considered for the job.
But Frenchman Renard is not willing to leave Saudi Arabia while Hugro Broos is also believed not to be interested.
McCarthy has been linked to the Bafana coaching job. He muddied the waters when he told foreign media he would be happy to accept the job that became vacant when Molefi Ntseki was sacked last month.
“We have no interest in letting Benni leave AmaZulu FC.
"He is doing a fantastic job‚ we are enjoying him and he is equally happy at AmaZulu‚,” Zungu said in his short but emphatic response to TimesLIVE on Tuesday.
Safa appears to be nowhere near appointing a new Bafana coach after they were reportedly snubbed by their top two preferred candidates‚ Pitso Mosimane and Carlos Queiroz, last week.
The soccer body was supposed to announce the man to take Bafana into the future last weekend but postponed the hugely anticipated press conference at the 11th hour‚ citing issues with international “Covid-19 travel" as the reason.
With no word on Mosimane and Queiroz‚ Safa are believed to have set their sights firmly on McCarthy‚ but Zungu has previously insisted they will resist attempts to destabilize the team.
South Africa is in Group G with neighbours Zimbabwe, Ghana and Ethiopia.
Bafana will first face the first trip to Zimbabwe in their opening fixture on 5-8 June before hosting group favourites Ghana, a week later between 11-4 June. Read Full Story