NEW YORK (CNN/Money) - The Bush administration is considering asking Federal Reserve Chairman Alan Greenspan to stay on the job for several months after his term expires Jan. 31, according to a published report Wednesday.

The Washington Post reported that the administration is mulling asking the chief of the nation's central bank to stay in place while the White House broadens its search for possible successors.

While Greenspan can not be named to a new term after his current term expires, the law allows a Fed governor to stay in place until a successor is confirmed by the Senate. Thus, if President Bush wanted Greenspan to stick around a bit longer, he could just put off nominating a replacement.

Greenspan refused to comment to the paper. White House spokesman Trent Duffy refused to speculate on the decision on the next Fed chairman, although he told the paper, "President Bush believes Chairman Greenspan is doing an excellent job."

While Greenspan is well regarded in global financial markets, delaying appointing a successor would bring a risk of added uncertainty about the direction of central bank policy, several Fed watchers told the paper.

The lack of a new nominee would be "a negative signal to the markets. . . . It implies that Greenspan is irreplaceable. It implies if we don't have Greenspan, everything will fall apart," said Kevin Hassett, director of economic policy studies at the American Enterprise Institute, a conservative think tank.

Sen. Richard Shelby, R-Ala., chairman of the Senate Banking Committee, told the paper that while he'd be happy if Greenspan could stay in the job for another decade because of his "exemplary" record, it's important for the administration to name a successor.

"An appointment would show decisiveness that (White House officials) are on top of the game, which I'm sure they are," he said.

If Greenspan were to stay in the job until May 11, 2006, he would become the longest-serving Fed chairman ever, exceeding the 18 years, nine months and 29 days served by William McChesney Martin Jr., from 1951 to 1970.