The price being discussed could not be learned.
The sources requested anonymity because the matter is not public, and a spokeswoman for Stifel and a spokesman for Barclays declined to comment.
Barclays has been reaching out to potential acquirers for the business for several weeks because it views it as non-core, sources told Reuters.
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Stifel Chairman and Chief Executive Ron Kruszewski has acquired several, mostly troubled retail brokerage and investment banking firms since 2005. The once low-key St. Louis firm that specialized in municipal bonds is now a national presence serving individual investors and middle-market companies.