A White House spokesman declined to comment.

The Biden administration has been looking for a director since Francis Collins retired in December 2021. The Senate must confirm the nominee. Until then, Lawrence Tabak, a longtime NIH administrator who had been principal deputy director, has been serving as acting director.

The position remains open as Republican lawmakers scrutinize the origins of Covid-19 and the NIH’s support for virus research at Chinese labs in Wuhan. In January, NIH advisers proposed strengthening oversight of virus research.

GOP lawmakers’ threats to curb government spending could hurt NIH funding, just as some of the agency’s most stalwart defenders in Congress have retired.

The search has stretched on so long that some potential choices aren’t interested, some of the people said, because a new director would have very little time to establish himself or herself in the post before a potential change in administrations could push that person out.

The short time remaining means the White House has begun to vet internal candidates for the post, the people said.

The Bethesda, Md.-based NIH, which has more than 18,000 employees and a $47.5 billion annual budget, conducts cutting-edge research into cancer, infectious diseases and drug abuse, while funding work by university scientists.

Discoveries by NIH scientists and grant recipients have spurred medical advances and been awarded more than 100 Nobel Prizes. During the pandemic, the agency’s vaccine researchers collaborated with vaccine makers and helped develop messenger RNA shots.

The agency’s director has historically been a prestigious and powerful position, attracting some of the country’s most decorated scientists.

Dr. Collins, who ran the agency under three presidents for more than 12 years, helped discover genes responsible for cystic fibrosis and other diseases. Harold Varmus, who led the NIH from 1993 to 1999, won a Nobel Prize for his research into genes that can mutate and cause cancer.

“While this position is one of the most important in the global scientific field, with all of the legal, political and financial hurdles, recruitment will remain challenging,” said Ellen Sigal, chairwoman of Friends of Cancer Research, a nonprofit that works with NIH to speed cures.

Most NIH directors have been white men, prompting the White House to make an effort to find someone with a different background, the people familiar with the search said.

Mary Klotman, dean of the Duke University School of Medicine, was a finalist last year, the people said. Dr. Klotman withdrew her name from consideration, however, because the process dragged on, people familiar with the matter said.

Dr. Klotman, an infectious-disease doctor who once worked in an NIH lab, didn’t respond to requests for comment.

Another woman who was a leading candidate also backed out, according to people familiar with the matter, who wouldn’t name her.

Among the factors that have complicated the search for a director is the Senate Health Committee, which would vet any choice and is led by Sen. Bernie Sanders (I., Vt.), who would be expected to disapprove of any potential candidate with ties to the pharmaceutical industry.

The position’s salary has also proved challenging, the people familiar with the search said. The job pays around $200,000 a year, less than the salaries of the people who run the various research institutes that make up the agency.

The salary is also much less than what potential candidates make running medical schools or serving in other life-sciences positions. Meantime, U.S. government ethics rules would require a nominee with pharmaceutical stocks or other kinds of stakes in companies to divest those positions.

Write to Liz Essley Whyte at liz.whyte@wsj.com and Stephanie Armour at Stephanie.Armour@wsj.com