CBA chief executive Ian Narev confirmed during a results presentation in August that a "range of third parties" were in discussions regarding CommInsure.
The bank's life insurance businesses, namely CommInsure and its New Zealand Sovereign business, are likely to be valued at around $4 billion.
According to a Reuters report, Hong Kong-based AIA Group is one of the final bidders for CBA's insurance division.
Zurich has also bid for the CBA assets, and is also in the race for ANZ's life insurance and wealth management business, according to the report.
ANZ chief executive Shayne Elliott has spoken about his desire to exit product manufacturing, which could be via a sale or a public listing.
Zurich is competing with US company Metlife on the ANZ assets, with both companies making bids by the Friday, 15 September deadline.
The outcome of the ANZ sale is likely to be announced within a month, while the CBA transaction is likely to take longer as more bidders are expected to join the auction, according to the report.
A statement by ANZ posted on the ASX yesterday said the bank would not comment on "speculation".
"The process is ongoing and ANZ remains in discussion with a number of parties as it continues to work through its options. This includes exploring capital market solutions to create a stand-alone business," said the ANZ statement.
"ANZ will continue to take a disciplined approach to this process and will update the market as appropriate."
A spokesperson for Zurich declined to comment about the auction process.