The heated conversation was leaked yesterday, a day after Mr Donovan told ABC Radio that Ms Redmond should step aside as leader and Ms Redmond admitted she had been asked to step down and consider taking the federal Senate seat left vacant by Mary Jo Fisher, who has resigned for health reasons.
In the recording, Ms Redmond becomes incensed when Mr Donovan asks her why she did not pledge any policies for his electorate.
She criticises Mr Donovan for relying on her as "the person to be recognised" during a visit to the Willunga markets.
A male voice, believed to be that of Liberal Terry Stephens, is heard telling Mr Donovan he must take responsibility for the loss himself.
"If you want to give me lip, step outside," a voice says.
The other male says: "Any time."
Ms Redmond has confirmed the recording.
A senior Liberal said the saga was a "worry" and had been "self created".