US Treasury Secretary John Snow is likely to step down in June, Republican sources said.
The US media have been speculating that Josh Bolten, who took over in April as White House chief of staff, wanted to replace Mr Snow with someone who could be a more forceful spokesman on the economy, preferably someone from Wall Street.
On Thursday, Mr Bush praised Mr Snow and said the Treasury chief has not indicated that he wanted to leave his post.
But people close to Mr Snow (66), a former industrialist who has served as Treasury chief for more than three years, have said he had long considered moving on prior to the November midterm elections.
The White House is narrowing its choices for a possible successor, with David Mulford, the US ambassador to India, seen as a strong contender, sources said.
Commerce Secretary Carlos Gutierrez and ex-Commerce chief Don Evans, a close friend of President Bush, are also among those whose names have been circulating for the Treasury position.
Other possible contenders who have been mentioned include Energy Secretary Samuel Bodman and former Bush economic adviser Stephen Friedman.