Botha is a former Springbok flyhalf who represented the national team 28 times between 1980 and 1992.
Mallett, who coached the Springboks between 1997 and 2000, played two tests for the Boks in 1984.
It is also reported that Willemse said "he can't work with people who undermine other people" and that he was "glad it happened on live TV so that people can see".
In a tweet, SuperSport said they are aware of the matter and they are looking into it.
A clip of the disagreement has gone viral on social media.