Spokesman Scott McClellan described Bush as actively in pursuit of the next Fed chairman. Greenspan's 18-year run on the Federal Reserve is expected to end on Jan. 31.
"As soon as possible," McClellan said when asked when Bush might choose a Greenspan successor. "The president will make a decision when he's ready to do so, but we are moving ahead on the nomination."
McClellan said the process had not been slowed by the focus in the past couple of months on Hurricane Katrina (search) and the nominations of John Roberts and Harriet Miers for the Supreme Court.
He called the Fed chairman position a "priority appointment" and said Bush was thinking about it very carefully and his staff had been working hard on potential candidates.
"The president's staff has been working very hard at looking at individuals to bring to his attention and he's been thinking about it as well," McClellan said.
"This is a priority appointment, the president is thinking about it very carefully and we continue to move forward on that nomination," he said. "I'm not going to speculate about the timing or any names."
Greenspan, 79, has signaled he prefers to retire when his term ends early next year, although the White House could ask him to stay on longer if a successor is not confirmed by January 31.
Asked about the Fed search process at a news conference on Tuesday, Bush said he had not yet seen a list of prospective nominees but would select a successor to Greenspan "at an appropriate time."
He also said he wanted to name someone who is viewed as independent from politics.
Three potential candidates are regularly mentioned -- Glenn Hubbard (search), a past adviser to Bush; Harvard economist Martin Feldstein (search); and Fed Governor-turned-White House adviser Ben Bernanke (search).
Other potential contenders include former Bush economic aide and ex-Federal Reserve governor Lawrence Lindsey (search), Fed Governor Donald Kohn (search), Fed Vice Chairman Roger Ferguson (search) and ex-Dallas Fed President Robert McTeer (search).