Kent has just 45 UK staff, but a deal would give Flowers the necessary UK bank licence to operate and expand.
There has been speculation that Flowers, which unsuccessfully bid for Northern Rock in 2007, is looking to create a new UK bank.
Kent confirmed the talks in a stock exchange announcement this morning.
The Financial Times had reported that New York-based Flowers would invest £50m into Kent and take a 49% stake.
Other reports have suggested that Flowers has identified up to ten other potential takeover targets.
Reports on the BBC website say that if Flowers is successful, it will be the first time that a private equity business has invested in a UK mutual lender.
Flowers, which appointed former head of the Financial Services Authority, Sir Callum McCarthy, as its European chairman, has also tried to buy Friends Provident.
The building society's short stock exchange announcement said: "Kent Reliance Building Society today announces that it is in talks with JC Flowers & Co to create a new corporate structure for the Kent Reliance business.
"If the new structure proceeds, it would allow for substantial new capital investment to support the business and would provide a means for the Society's members to remain members of a mutual organisation."
