WASHINGTON—As Hurricane Florence was forming in the Atlantic, senior Trump administration officials considered replacing the head of Federal Emergency Management Agency amid allegations that he misused resources traveling to his home in North Carolina, according to people familiar with the matter.

FEMA Administrator Brock Long is the target of an internal investigation looking into frequent travel between the nation’s capital and his home in Hickory, N.C., according to people briefed on the probe. The investigation included surveilling Mr. Long as he was driven 400 miles each way on his commute, the people said.

Investigators have told administration officials that Mr. Long, while under surveillance, often left agency headquarters on Thursdays and traveled home with a caravan of federal workers, who stayed in nearby hotels for the long weekend, the people said. He has spent about 150 days in North Carolina since he took over the job last year, which included weekends and time-off, the people said.

Mr. Long declined, through a spokeswoman, to comment on Friday. He has previously denied any wrongdoing and he didn’t attend a pair of FEMA news conferences Friday afternoon about the storm.

The White House has begun discussing potential replacements for Mr. Long, a senior White House official said.

As Florence continues to deluge the U.S., here's what you need to know about the dangerous East Coast storm. Photo: Reuters

At a media briefing on Thursday, Mr. Long said he “would never intentionally run a program incorrectly” and pledged to cooperate with the investigation, and that he and the agency were “100% focused” on the approaching storm. “That’s exactly where our attention needs to be from the standpoint of the life safety mission,” he said.

The Department of Homeland Security inspector general is also reviewing communications between Mr. Long and a FEMA contractor that appear to include discussions about future employment, said one of the people briefed on the investigation. Investigators are also looking into an accident involving an SUV, owned by the federal government and used to transport the director, that wasn’t property reported, the person said.

Mr. Long was informed last fall by DHS attorneys and the inspector general that his trips home violated the law, the people said. The inspector general’s office has told administration officials that they tailed Mr. Long’s caravan to determine whether he was using federal resources to return home despite the warnings, the person briefed on the investigation said.

The inspector general’s final report is expected in the coming days, but preliminary findings have been shared with DHS Secretary Kirstjen Nielsen, administration officials said. The existence of the investigation was first reported by Politico on Thursday.

Ms. Nielsen brought details of the preliminary findings to Mr. Long and urged him to resign if the allegations were accurate, one administration official said. Another official familiar with the situation disputed that the secretary made that suggestion to Mr. Long.

A DHS spokesman declined to address the allegations, referring questions to the inspector general’s office. The inspector general’s office didn’t respond to requests for comment.

“At this time, we are fully focused on preparing for, responding to, and recovering from Hurricane Florence and the storms in the Pacific,” DHS spokesman Tyler Houlton said in a statement. “The secretary is confident in the leadership at FEMA and their proven disaster management ability.”

Senior White House officials discussed replacing Mr. Long in the past several days, according to one person familiar with the matter. White House Chief of Staff John Kelly ultimately decided to leave Mr. Long in place until the final report was available, the person said. A White House spokeswoman declined to comment.

President Trump has been meeting with Mr. Long regularly in recent days as Hurricane Florence prompted flooding and heavy rains on the Southeast coast. On Tuesday, Mr. Trump praised his FEMA director as someone “who’s done so well for us” during storms that hit Texas and Florida last year.

Inside FEMA, Mr. Long is well liked. Several FEMA officials said privately that they felt conflicted about reports of his travel.

One FEMA official said Friday the administrator has national-security duties, and the use of government vehicles supports that effort and allows for him to ensure classified communication. The official also said that in previous administrations, using vehicles in a similar fashion was routine practice. Officials were working to resolve any discrepancies in the use of specialized vehicles and federal laws, the official said.

Mr. Long joined the administration when Ms. Nielsen was chief of staff at DHS and Mr. Kelly was the secretary. Previously, Mr. Long was an executive at Hagerty Consulting, an Illinois-based emergency-management consulting firm with offices in Washington. Mr. Long also ran the Alabama Emergency Management Agency and was an emergency-management official in Georgia. He also has previously worked at FEMA.

Mr. Long is the latest Trump administration official to face questions about improper use of federal resources while traveling.

Scott Pruitt, the former EPA administrator, resigned in July amid allegations of ethical lapses and improper spending, including $163,000 on first-class flights, military aircraft and charter flights. Health and Human Services Secretary Tom Price resigned last September over his extensive use of private jets and military flights.

—Ben Kesling contributed to this article.

Write to Michael C. Bender at Mike.Bender@wsj.com