The DA laid charges of extortion, bribery and corruption against Mduduzi Manana on Monday.
According to EWN, the party now wants the police to investigate the audio clip in which Manana can be heard offering Christine Wiro R100,000 to drop the case.
Wiro, who was Manana's former domestic worker, laid a complaint of common assault against him last week, after she claimed he pushed her down the stairs at his Fourways home.
The DA's Terri Stander says the DA will not rest until Manana is behind bars.
"Cyril Ramaphosa and Mduduzi Manana belong to the same WhatsApp group. They're both in the ANC, and I'm certainly not seeing any decisive action there."
Prior to the DA laying charges, Manana said that he would be opening a case against Wiro, claiming that she tried to extort R100,000 from him. However, the police say that there is still no record of such a case.