San Francisco Fed President Williams is leading candidate to become next President of the New York Fed, sources said.
The Federal Reserve had been expected to raise its benchmark interest rate a quarter point to a target range of 1.25 percent to 1.5 percent.
Mohamed El-Erian is being considered by the White House for Fed vice chairman.
Replacing New York Fed President Bill Dudley may be one of the most controversial Fed appointments in recent memory.
NY Fed President William Dudley, a key figure in managing the financial crisis and its aftermath, announced his retirement.
"But every one-tenth of 1 percent is producing jobs, and it would be a shame not to do it," JPMorgan's Jacob Frenkel adds.
"Janet is a safe pair of hands," Stanley Fischer tells CNBC on his last day as vice chairman of the Federal Reserve.
a narrowing U.S. trade deficit in August lifted the dollar index as gold flattened.
Stanley Fischer's decision to step down from the Fed is part of a new era that increasingly looks like it won't include Janet Yellen.
The dollar fell against a basket of currencies after Federal Reserve Vice Chairman Stanley Fischer announced his resignation.
Fed Vice Chairman Stanley Fischer's decision to step down creates another opening at the central bank for President Trump to fill.
Fed Vice Chair Stanley Fischer said low rates send "a powerful signal that the growth potential of the economy may be limited."
Trump appears ready to remake the Fed in an image that will be considerably different than what investors have known for many years.