I heard this while on a tour of the Denver Mint. I asked the tour guide to repeat it, because I always thought there were twelve. He said there were 12 main banks and 25 branch banks. So I went hunting. The only evidence I've found so far is a PDF-format document on the Federal Reserve web site (specifically, in the "Overview" section on the Purposes & Functions page).
An excerpt from that page:
A network of twelve Federal Reserve Banks and their twenty-five Branches carries out a variety of System functions...
A table, from a few pages farther along:
|8||H||St. Louis||Little Rock
|12||L||San Francisco||Los Angeles
Salt Lake City