The regional Fed banks, while overseen by the Board of Governors in Washington, are actually quasi-private institutions, technically owned by local private banks. The regional Fed banks contribute to monetary policy making and in the case of the New York Fed, implement it, while also regulating local banks and providing services to financial firms. They are not currently officially subject to FOIA, as the Board is.

In a press release, Sen. Warren's office said the law would make sure the regional Fed banks are responsive to congressional inquiries. Both senators have for some time pressed the central bank for various documents about ethics issues and other matters and have said the banks they have contacted have not been responsive.

The law would also fortify the central bank's Office of Inspector General, its in-house watchdog, which is currently investigating the financial market trading of several regional bank leaders, both retired and currently serving. Earlier this year, the Inspector General cleared Fed leader Jerome Powell and his former second-in-command Richard Clarida of trading violations, even as critics like Better Markets have questioned the thoroughness of the inquiry.

The Fed Inspector General is named by the Fed leader, and the proposed law would change that to make the investigations chief a presidential appointment subject to Senate confirmation. The law would also deny all government financial regulatory agencies the ability to refuse congressional requests for ethics-related information.

Warren's office said the law "would strengthen congressional oversight of the Fed and other financial regulatory agencies."

A spokesperson from the Fed declined to comment on the legislation.

At least one Fed watcher was doubtful the legislation has a future. Krishna Guha, an analyst at Evercore ISI, told clients, "we see this bill as unlikely to pass but it has enough bipartisan interest to attract ongoing attention."