It is unclear how much cash the insurer might hope to raise, or what value the possible offer might place on the firm.
The source said CBL could be the second company to float on the NZX this year after transport and logistics operator Fliway Group, which expects to list on April 9.
The company, founded over 40 years ago, has 100 staff working in eight offices across four continents.
It has customers in 25 countries.
CBL is chaired by Sir John Wells, who is also the chairman of Fisher Funds, Bancorp and Auckland Council Property.
Sir John is the father of New Zealand broadcaster Jeremy Wells.
CBL managing director Peter Harris said in a statement that the firm was a considerable exporter of financial services, with much of its revenue generated outside New Zealand, largely in Europe.
The final two sentences of the press release suggest an IPO and listing is imminent.
"CBL shares cannot currently be applied for or acquired under any intended offer," the company said. "If an offer is made, it will be made in accordance with the provisions of the Financial Markets Conduct Act 2013."
CBL's largest shareholder is Singapore-based Oceanic Securities, with a 32.4 per cent stake, according to the Companies Office.
Ellerslie-based Federal Pacific Group, owned by CBL deputy chairman Alistair Hutchison, has a 30.8 per cent holding.
Read more about CBL from its website here:
