Lew, who previously served as budget director under Obama and former president Bill Clinton, has long been considered the frontrunner to replace Geithner, the last remaining member of Obama's first-term economic team.
White House spokesman Jay Carney declined to comment on news reports of Lew's prospective move, but praised him as "a remarkably capable chief of staff" and an "exceptional public servant".
As with so many presidential aides, the Treasury Secretary's primary goals are "economic growth and job creation", he said.
A former investment banker and Capitol Hill aide, Lew was instrumental in crafting the August 2011 debt deal that created the $600 billion automatic tax increases and spending cuts narrowly avoided in the New Year's "fiscal cliff" agreement.
A 57-year-old native of New York City, Lew's long familiarity with Capitol Hill began when he took a job as a legislative aide in 1973.
He went on to serve for nine years as chief domestic policy adviser to House Speaker Tip O'Neill.
While Lew's announcement could come as soon as Thursday, it was not clear that the president has settled on his new choice for chief of staff, according to CNBC.
Deputy National Security Adviser Denis McDonough and Ron Klain, former chief of staff to Vice President Joe Biden are both seen as potential Lew replacements.
News of Lew's appointment came as Labour Secretary Hilda Solis announced she would not return for Obama's second term that starts Jan 20.
Meanwhile, USA Today cited White House officials as saying three other Cabinet members will be staying -- Attorney General Eric Holder, Veterans Affairs Secretary Eric Shinseki and Health and Human Services Secretary Kathleen Sebelius.
Late last month, Obama nominated Senator John Kerry to be Secretary of State. Earlier this week, in two controversial choices, he picked former Republican senator Chuck Hagel for Defence Secretary and White House Adviser John Brennan to lead the Central Intelligence Agency (CIA).
(Arun Kumar can be contacted at email@example.com)