Dudumashe landed in hot water last month after she shared a social media post that defended Manana's character only a few days after allegations emerged that he had assaulted a woman outside a Johannesburg bar.
After the public backlash, the radio and TV personality deleted the post and issued a public apology.
SABC spokesman Kaizer Kganyago said: "No formal investigation into her conduct has been launched but we have been in discussions with her to deal with the matter internally."
Responding to fans' inquiries on social media, Dudumashe said she did not know when or if she would return to her slot on Metro FM.
She was also criticised for comments she made at a discussion on gender-based violence at the University of Venda, in Limpopo, last month.
Dudumashe asked men in the audience to stand, reportedly advising those unsure about whether to stand to look between their legs.
She has apologised for her comments and has declined a nomination to the board of the SA National Aids Trust because of the controversy she has attracted.
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