After Orlando Pirates beat Polokwane City 2-1 on Tuesday to go top of the log, Zungu, a self-confessed Bucs fan, caused a stir on Twitter by claiming Buccaneers assistant coach Mokwena was ‘making Pirates a top team again’.
The former Sundowns midfielder also indicated Mokwena, who left the Brazilians for Pirates prior to last term, was directing affairs in Mosimane's shadow when the league champions clinched continental honours in 2016.
Zungu's utterances were deemed as disrespectful to Downs head coach Mosimane and Sea Robbers counterpart Milutin 'Micho' Sredojevic by some, including Cape Town City tactician Benni McCarthy.
Zungu, who now plies his trade for Amiens in France, later apologised for any offence caused.
Asked about the matter, Mosimane said: "I am not on social media. I would like to be on social media so that I can tweet. I think you can have enough numbers if I tweet.
"I don't know about that, they told me. Really, do I need to go there? Whether Rhulani was here we won trophies; when he was not here we win trophies. What was my last comment about Rhulani? You can google all my comments. I don't want to spoil that. I said he is going to be better than me in future. He has potential."
Mosimane, whose side remain unbeaten in the Absa Premiership this season following a 3-1 win over Free State Stars last night, went on to give Sredojevic credit for his work at Mayfair.
"I want to stay positive. Probably Manqoba [Mngqithi] would like to answer that, the assistant coach? I want to speak with Micho ... Micho has done exceptionally good work with Orlando Pirates; brilliant work for the last two years. Whether it's him coaching the team or not, I don't know. It's not for me to focus on that."
Mosimane added: "I like Rhulani, I have a soft spot for Rhulani. I have a soft spot for Orlando Pirates because I wore the badge. The chairman [Irvin Khoza] is a good chairman, you can hear when he speaks about me. If I want to respond I can respond you know."
Sundowns, in third spot on the log, are set to host Pirates at Loftus Versfeld on Saturday in what is expected to be a thrilling match.