Treasury Secretary Timothy F. Geithner, an architect of the Obama administration’s economic strategy, has told the president that he may seek as soon as this summer to resign, according to people familiar with the matter.

Geithner’s departure would mark the loss of Obama’s longest-serving economic adviser at a time when the recovery has slowed and the unemployment rate remains stubbornly high.

Geithner has told the White House he will wait until the conclusion of talks with Congress over the nation’s debt before deciding whether to leave, according to the people familiar with the matter.

An administration official said Geithner recognizes the conclusion of these negotiations could provide a “window” for him to leave. Another official at the Treasury Department said Geithner doesn’t plan to make any decisions while he is focused on striking a deal with lawmakers to reduce the deficit and raise the federal limit on borrowing, which he has said must happen by Aug. 2 to avert a catastrophic default.

These two officials spoke on the condition of anonymity because they were discussing Geithner’s private deliberations.

When asked about his career plans late Thursday, Geithner said at a conference in Chicago that “I’m going to be doing this for the foreseeable future.”

But he acknowledged that family concerns were weighing on him. Geithner said his family was moving back to New York, where his son would finish high school. Geithner said he would commute to Washington.

“I’ve never had a real job,” Geithner told his interviewer, former president Bill Clinton. “I’ve only worked in public service. I live for this work.”

When discussing his future in other settings, Geithner has said he would be ready to leave the administration as soon as the president would allow him and a successor could be identified, according to a person familiar with the matter.

A departure would come at a sensitive time for Obama. The president would have to find a replacement in a highly charged political environment. The White House has been slow to nominate senior financial policymakers, and congressional Republicans have blocked several top nominees.

If Geithner left this summer, he also would be leaving in the hands of his successor critical matters such as the nation’s housing policy, the future of mortgage financiers Fannie Mae and Freddie Mac, and the design of regulations overseeing large financial firms.

Geithner is the last remaining member of the president’s original economic team. His departure would follow the recent announced exit of Austan Goolsbee, chairman of the Council of Economic Advisers. And it would bring new emphasis to National Economic Council director Gene Sperling, a former Treasury counselor who is reprising a role he held in the Clinton administration.

During his tenure, Geithner has continually won over Obama in contentious policy debates. He shaped the president’s response to the financial crisis, successfully arguing that the government should not seize struggling banks.

More recently, he urged Obama to propose cutting the annual deficit by $4 trillion over 10 years, despite other top advisers advocating that the president focus squarely on the nation’s high unemployment.

Geithner, who will turn 50 in August, was one of the architects of the Wall Street bailout in the fall of 2008 and faced sharp criticism in his first year as Treasury secretary, including calls for his resignation. He has been accused of protecting the bonuses of Wall Street traders while paying insufficient attention to the nation’s foreclosure epidemic. And at times, he hasn’t seemed responsive to the political demands of Washington.

Geithner has fared better as the financial system has stabilized, emerging as one of Obama’s most trusted confidants.

Bloomberg News first reported Thursday evening that Geithner has signaled to the White House that he is considering leaving.

A new Treasury secretary would need a mix of political and diplomatic skills to simultaneously manage tense and delicate negotiations on deficit reduction at home, an ongoing debt crisis in Europe, and the evolution of a tricky economic relationship with China.

And while experience in the financial industry has long been viewed as preparation for the job of Treasury secretary, in the post-crisis era a Wall Street pedigree could prove toxic.

In the past, analysts have discussed Roger Altman, an investment banker and deputy Treasury secretary in the Clinton administration, and Erskine Bowles, a former Clinton chief of staff who co-chaired Obama’s deficit reduction commission, as possible candidates for the top Treasury post. Another Democratic economist popular with business is Laura Tyson, a business school professor at the University of California at Berkeley who served as chairman of the Council of Economic Advisers under Clinton.

Inside the Obama administration, budget director Jacob J. Lew or chief of staff William M. Daley could be viewed as qualified for the job, but the appointment of either would leave another big hole to fill. Gary Gensler, the chairman of the Commodity Futures Trading Commission, could also emerge as a candidate. Sheila Bair, the outgoing chairman of the Federal Deposit Insurance Corp., would be a dark-horse candidate.

The president may yet convince Geithner to stay. Any nomination hearing could raise the specter of a protracted and nationally televised confirmation hearing unfolding in the midst of the 2012 election campaign.

“It’s going to be an opening for the Republicans to put the Obama economic policies on a big public trial,” said Kevin Hassett, an economist at the conservative American Enterprise Institute. “Because of that, it’s likely to be one of the more dramatic confirmations in modern history.”

Geithner is the only Treasury secretary to have essentially launched his career at the agency. He was a mid-level staffer when then-Treasury Secretary Robert Rubin plucked him for a high-profile job in the 1990s. He rapidly rose through the ranks.

After the Clinton administration, he served at the International Monetary Fund and as head of the Federal Reserve Bank of New York, where he oversaw both the collapse and the first stages of the rescue of Wall Street.

When he interviewed with Obama to be Treasury secretary, he made the case against joining the administration, saying he would be at odds with Obama’s “change” message. But Obama selected him anyway.

Jared Bernstein, former economic adviser to Vice President Biden, said finding a nominee to replace him could be a challenge, given the confirmation process. Asked who might step up, Bernstein joked, “A very smart, well-versed economic masochist.”

Staff writers Neil Irwin and Peter Wallsten contributed to this report.