WASHINGTON – 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 among 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 in recent weeks, and she is seriously considering accepting the nomination, according to the people, who requested anonymity in order 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 the woman many once considered to be a shoo-in for the position, Janet Yellen, currently the vice chair at the central bank.

That has turned what typically has been an uncontroversial appointment into a political lightening 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 must fill as many as four open seats on the central bank’s board. Two of them were held by women: Fed Gov. Elizabeth Duke resigned at the end of last month, while Fed Gov. Sarah Bloom Raskin has been nominated as deputy secretary at Treasury.

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 replacement will be selected by the bank’s board of directors.)

Brainard worked under White House economic adviser Gene Sperling when he served in the same role during 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 of 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.