The offering will consist of a sale of existing shares in the form of global depository receipts (GDRs) by shareholders, Kaspi.kz said in a statement on Monday.
Kaspi.kz is a major player in Kazakh payment systems and e-commerce, while Kaspi Bank is a retail-focused lender.
Its listing would boost London's stock market, where few companies have tried to list in the past three months due to uncertainty over Britain's European Union departure.
But there are signs of a pick-up, with African telecoms firm Helios Towers announcing plans to float last week.
"Our intention is that it (the IPO) would be completed in the fourth quarter," Kaspi.kz chief executive Mikheil Lomtadze told Reuters by telephone.
Lomtadze declined to comment on the size of the listing, but a source familiar with the deal said it was targeting a valuation of around $5 billion, with a minimum offering size of $500 million to $600 million.
The selling shareholders include Baring Vostok funds, Goldman Sachs, Kaspi.kz board chairman Vyacheslav Kim, and Lomtadze.
"Each of the selling shareholders intends to retain shareholdings in the company post-IPO," Kaspi.kz said.
Morgan Stanley, UBS, Citigroup and Credit Suisse are acting as joint global coordinators on the offering, along with Renaissance Capital as joint bookrunner.
Previous foreign listings of Kazakh banks have turned out to be risky investments. Of the four local lenders which have listed on foreign bourses, only Halyk Bank, Kazakhstan's biggest bank by assets, continues to trade in London.
Two other Kazakh banks, KKB and Alliance, have delisted as they were bailed out and taken over by other lenders.
Another, Astana Banki (Bank of Astana), lost its licence last year, less than a year after a secondary placement in Moscow.
(Reporting by Olzhas Auyezov and Abhinav Ramnarayan; editing by Jason Neely and Alexander Smith)
