White House staff members will be among the first to be vaccinated.

White House staff members who work in close quarters with President Trump have been told they are scheduled to receive injections of the coronavirus vaccine soon, at a time when the first doses of the vaccine are being distributed only to high-risk health care workers, according to two sources familiar with the distribution plans.

The goal of distributing the vaccine inside the West Wing is to prevent additional government officials from falling ill in the final weeks of the Trump administration. The hope is to eventually distribute the vaccine to everyone who works in the White House, but will begin with some of the most senior people who work around the president, one of the people said.

It is not clear how many doses are being allocated to the White House, or how many are needed. While many Trump officials said they were eager to receive the vaccine and would take it if it were offered, others said they were concerned it would send the wrong message by making it look like Trump staff members were hopping the line in order to protect a president who already had the virus and has bragged that he is now “immune.”

The first doses of the Pfizer-BioNTech vaccine left a facility in Michigan early Sunday, with UPS and FedEx teaming up to ship them to all 50 states for distribution. A White House spokesman did not respond to a request for comment.

The White House has seen multiple waves of coronavirus cases. Mr. Trump, the first lady and a half-dozen advisers tested positive at the end of September and early October. A few weeks later, Vice President Mike Pence’s chief of staff, Marc Short, and a handful of other Pence staff members and advisers got sick.

And a third wave hit the West Wing after the president’s election night party at the White House. The White House chief of staff, Mark Meadows, got sick around that time, as did a number of other Trump advisers.

Since then, some senior Trump advisers have left the White House, like the senior communications adviser, Alyssa Farah. But the president’s core circle of top staff remains.