Geithner had told the White House he was not willing to serve in a second term. Others leaving Obama's first term cabinet are Hillary Clinton and Leon Panetta.
Though there has been no announcement of the nomination by the White House, Bloomberg News Service has said that Obama plans to announce the nomination on Thursday.
The next treasury secretary will play a leading role in working with Congress to raise the government's $16.4 trillion debt ceiling.
Sources familiar with the process say Obama is choosing Lew because of his wide variety of government and private sector experience. Lew previously led the Office of Management and Budget and oversaw international economic issues at the State Department.
He has played a key role in numerous financial negotiations between the White House and Congress.
The sources spoke on the condition of anonymity in order to discuss the expected nomination ahead of the president.
(With agency inputs)