It has also been reported that Kirsten may coach IPL team Mumbai Indians in the fifth edition.
The report said that Kirsten has hired an Australian agent to look into the opportunities in Sydney.
The two teams with whom 'discussions have already taken place' are the Sydney Sixers franchise and the Sydney Thunder.
"We've had initial conversations in respect to Big Bash coaching opportunities," Kirsten's agent Peter Lovitt, said.
"Gary has a great respect for cricket in Australia, and sees a coaching role as an exciting appointment. I'm sure a coach of his high credentials would be a great asset," Lovitt was quoted as saying by 'Sydney Morning Herald'.
Kirsten, who decided against extending his contract with the Indian team, has confirmed that South Africa have approached him for the job.
"They have approached me but I've said I'm not going to make any decisions just yet. I need to take some time off and clear my mind for a while after this magnificent journey," Kirsten told 'The Guardian'.