The division offers services including current accounts, deposits and mortgages, as well as a variety of products including life insurance and wealth management. The business has a network of 74 branches across France.
If a deal is agreed, Barclays will continue to operate its corporate and investment banking operations in France.
Nassim Cherchali, director of AnaCap, said: “This is an opportunity to acquire an attractive and established banking operation built on a team of highly talented individuals with exceptional relationships with customers across France.
"We have already established an unrivalled track record within the private equity industry for acquiring and growing banking platforms across the continent and, if concluded, we look forward to building this business further in a market with significant potential for innovation and expansion.”
Barclays this morning revealed that pre-tax profits fell by almost a quarter year-on-year as the investment bank division struggled to perform.
It is also in talks over its Africa division, with former boss Bob Diamond confirming yesterday that he has thrown his hat into the ring.
The lender is offloading its non-core divisions under new chief executive Jes Staley, who last month revealed a major restructure of the struggling bank.
Under the new plan, Barclays has been split into two, main core divisions - Barclays UK and Barclays Corporate and International.