The AFR reported Australian funds management sources as saying FlexiGroup would carry out an equity raising to fund its purchase of the finance company.
In addition to FlexiGroup, other bidders for F&P Finance have included local private equity firm Maui Capital and Australian players Archer Capital and CHAMP private equity, according to reports. US private equity giant KKR has also reportedly been involved in the bidding.
Fisher & Paykel Finance, whose products include Q Card and Farmers Finance, is owned by whiteware manufacturer Fisher & Paykel Appliances, which was acquired by Chinese home goods maker Haier in 2012.
The finance business was never central to the Qingdao-based firm's aims.
Haier made the acquisition largely to secure a more upmarket whiteware brand for its portfolio, as well as to gain access to the New Zealand company's research and development capabilities.
Fisher & Paykel Appliances announced in May that it had appointed investment bank First NZ Capital to "assess potential options" for the future of its finance arm "in response to recent market interest".
At that time chairman Keith Turner said interest from potential buyers had been strong.
"Whilst [the company] is happy to continue to own FPF and support its ongoing development, it is very possible a change in ownership may be a better option," Turner said.
Fisher & Paykel Finance's other businesses are Consumer Insurance Services, which provides insurance and product protection policies to retailers and consumers, and Equipment Finance.
In April Fisher & Paykel Appliances reported a full-year loss of $12.6 million for the 2014 calendar year, an improvement on the $31 million loss it reported a year earlier.