John Williams, president of the Federal Reserve Bank of San Francisco.

It would make sense if the U.S. economy continues to grow for the Federal Reserve to begin trimming its $4.5 trillion balance sheet towards the end of this year, unwinding extraordinary stimulus deployed during the crisis, a Fed policymaker said on Thursday.

John Williams, president of the San Francisco Federal Reserve Bank, said this process would take several years and run in parallel, albeit for longer, to increases in the Fed's interest rates.