The national team's coaching job became vacant after Stuart Baxter resigned earlier this month and Molefi Ntseki was appointed on an interim basis.
The South Africa Football Association (Safa) is still looking for a replacement for the British tactician.
Meanwhile, Zondo feels current Sundowns coach Mosimane deserves another chance to lead Bafana Bafana ahead of the 2021 Africa Cup of Nations (Afcon) qualifiers which will start in October 2019.
“For me, we have tried everything. We brought Carlos Parreira, who was supposed to be the best," Zondo told SABC.
"We had the lowest of the lowest [Joel] Santana, we had Carlos Queiroz, we had Stuart Baxter. Are we happy? We are not."
The former Lamontville Golden Arrows coach urged Safa to entrust Mosimane with the responsibility of restoring Bafana back to the pinnacle of African football.
"We are not even happy with our own. Why don’t we continue with our own and have trust in them? Give them the necessary support, because when we go down we go down as a nation," he added.
"Give the same support as the coaches who come from outside, whether we win or lose because other countries are doing it. I have not seen a World Cup coach that wins as a foreigner.
"Why don’t we try our own here? How many Cups has Pitso won? Probably at the moment, he is the top, and that should be appreciated by saying he should take the job and give him the necessary support,” he concluded.
Mosimane was appointed Sundowns coach after he was sacked by Safa in 2012 and he transformed the club into one of the top teams on the African continent.