According to the report, the recording is damaging to Zuma as it disproves his claim that he never got the chance to tell his side of the story during the investigation.
This could be seen as another retaliation against the investigation by Zuma.
The charge comes after Zuma revealed on Friday that we would actually take Madonsela's report on state capture on judicial review, which effectively means fighting it out in court.
Madonsela released her report titled "The State Of Capture" on 14 October this year, days before her term expired.
Mkhwebane is quoted in the Sunday Times report, as saying there should be an investigation whether Madonsela violated section 7 (2) of the Public Protector Act.
The act stipulates that "no person shall disclose to any person the contents of any document in the possession of a member of the Office of the Public Protector or the record of any evidence given before the public protector ... during an investigation, unless the public protector determines otherwise".
Madonsela released the tape after her run as Public Protector and a source in the presidency is quoted saying she had no permission to do so.