White House officials would not confirm that a final decision had been made, but aides did not dispute that Lew was emerging as the consensus choice. An announcement was expected Thursday as the administration moves to fill the most critical Cabinet jobs for Obama's second term.
White House Press Secretary Jay Carney praised the expected nominee: "Over the past more than quarter of a century, Jack Lew has been an integral part of some of the most important budgetary financial and fiscal agreements, bipartisan agreements in Washington."
Obama already has nominated Sen. John Kerry to succeed Hillary Rodham Clinton at the State Department, former Sen. Chuck Hagel at the Defence Department and counterterrorism adviser John Brennan as the new CIA director.
Obama's choice of Lew is seen as a signal of the president's determination to control record-breaking budget deficits.
The 57-year-old Lew would bring private sector and international experience to the Treasury Department. He has held top jobs at Citigroup's wealth management branch and at the State Department, where he oversaw international economic issues in his first job for Obama.
Lew has spent much of his career mastering the mechanics of the federal budget, including two stints at the helm of the Office of Management and Budget, once under Obama and also under former President Bill Clinton.
That background could help shape the Obama administration's strategy in upcoming talks with congressional Republicans over raising the federal government's $16.4 trillion borrowing limit, which will allow the U.S. to pay its bills. Republicans are expected to demand deep budget cuts in return. The federal debt limit is expected to be tapped out sometime in February.
At the beginning of March, $110 billion in cuts to military and domestic programs will automatically kick in if no congressional budget deal has been reached by then. Congress and the administration postponed that issue in the so-called "fiscal cliff" agreement that received final congressional passage on Jan. 1.
The third pressing deadline will occur March 27, when a congressional resolution that is keeping the government operating without a budget will expire. Without a new bill, the government would shut down.
A person familiar with the selection process said Lew's budget experience was particularly important to the president, given the treasury secretary's key role in co-ordinating with European allies on the continent's debt crisis, among other global financial matters.
Unlike Geithner, however, Lew appears to have no obvious China-related background. It had been expected that Geithner's experience living and studying in China would help him in dealings with what has become the world's second-largest economy. Geithner started off by saying before his confirmation that the Obama administration thought China was "manipulating" his currency.
Lew, an observant Jew who does not work on Saturday, is well-liked in Washington by both Democrats and Republicans and well-respected by staffers at the White House, where he has served as chief of staff since January 2012.
A pragmatic liberal, Lew has also been a key player in several negotiations between the White House and Congress, including the recent talks to avert a fiscal crisis.
If confirmed by the Senate, Lew would replace Geithner, who plans to leave around Obama's Jan. 21 inauguration. Lew is expected to be easily confirmed by the Democratic-led Senate.
The sources spoke on the condition of anonymity in order to discuss the expected nomination ahead of the president.
Lew's immersion in the minutiae of federal budgets contrasts with the experience of most previous Treasury secretaries. Many arrived from high-level posts on Wall Street, where they presided over securities trading and investment banking.
"I think Wall Street would have preferred someone with more financial market specialization, but Lew is being brought in because he knows the budget," said David Wyss, a former chief economist at Standard & Poor's. "Clearly, Obama has decided that his priority in a second term will be the budget."
Lew's nomination would also signal Obama's intent to keep Treasury close to the White House sphere as Obama engages with Congress on fiscal issues and as the administration continues to implement key aspects of the financial regulation overhaul that Geithner helped shepherd into law in 2010.
Associated Press writers Julie Pace, Jim Kuhnhenn and Martin Crutsinger contributed to this report.