Lael Brainard, undersecretary of the Treasury for international affairs, sits beside Timothy Geithner, then Treasury secretary, left, and deputy national security adviser Michael Fromer during a June meeting with President Obama in the Oval Office. (Pete Souza/The White House)

The White House is considering nominating a top female official at the Treasury Department to fill one of the vacant seats at the Federal Reserve, according to two people familiar with the process, amid criticism over the role of women in the Obama administration.

As undersecretary for international affairs, Lael Brainard is one of the most highly ranked — and most visible — female members of President Obama’s economic team. Her name has long been circulated in the insular world of Fed watchers as a potential candidate to sit on the central bank’s influential board of governors.

But her conversations with the administration have ramped up recently, and she is seriously considering accepting the nomination, according to the two people, who requested anonymity to discuss personnel issues. The White House declined to comment.

Brainard’s nomination could help solve a public-relations problem for the White House, which has been assailed over the lack of women in premier posts. Obama is weighing whether to name Lawrence H. Summers, a close former adviser, to the top job at the Fed — a move that would mean passing over Janet Yellen, the vice chair at the central bank whom many once considered a shoo-in.

That has turned what typically has been an uncontroversial appointment into a political lightning rod. The National Organization for Women has decried what it called a “sexist whispering campaign” against Yellen, and 20 Senate Democrats, including key members of the banking committee, sent a letter to the White House urging Obama to appoint her. Summers also has been dogged by accusations of gender bias after suggesting while he was president of Harvard University in 2005 that women were not as talented as men in math and science, a statement he later called an act of “spectacular imprudence.”

In addition to naming a new chair for the Fed, Obama could fill up to four seats on the central bank’s board. Two of them were held by women: Fed governor Elizabeth A. Duke resigned last month, and governor Sarah Bloom Raskin has been nominated as deputy secretary at Treasury. Governor Jerome H. (Jay) Powell’s term ends in January, but he could continue serving. If Yellen is not nominated for the top job, she is not expected to stay at the Fed. (Another top female official, Cleveland Fed President Sandra Pianalto, is retiring in January, but her successor will be selected by the bank’s board of directors.)

Brainard worked under White House economic adviser Gene Sperling when he served in that role in the Clinton administration. She then moved to the Brookings Institution to work on global development issues before returning to Treasury in 2010 as the agency’s highest-ranking woman at the time. As the head of the department’s international affairs division, she has been on the front lines dealing with the European crisis, pushing for tough requirements before debt-saddled countries are thrown financial lifelines.

Brainard’s confirmation for her Treasury post in 2010 was delayed by concerns over late payments of property taxes. She was eventually confirmed in a bipartisan vote.

Obama could nominate at least one more woman to the central bank. The two people, who are also familiar with Brainard’s consideration for the Fed, said Janice C. Eberly, a former senior economist at the Treasury and now a professor at Northwestern University’s Kellogg School of Management, is also under consideration. But they were unsure how far the discussions at the White House over Eberly had progressed.

It was also unclear whether the announcements would be made at the same time Obama names his pick to lead the Fed. That decision is expected in the coming weeks, though the escalating turmoil in Syria could delay it.

Zachary S. Goldfarb contributed to this report.