WASHINGTON—President Trump is considering new high-level staff changes in his administration—including discussing a potential successor for White House Chief of Staff John Kelly—as the West Wing makes preparations for the start of the final two years of Mr. Trump’s current term.

The first to go is expected to be the deputy national security adviser, Mira Ricardel, who has clashed with First Lady Melania Trump. Mr. Trump is also leaning toward the ouster of Homeland Security Secretary Kirstjen Nielsen, who is a close ally of Mr. Kelly, White House officials said. The president has decided to replace Ms. Nielsen, but hasn’t finalized the timing, White House officials said, in part because there isn’t an obvious candidate to replace her.

Mr. Trump has told aides that he is aware that forcing out Ms. Nielsen may result in Mr. Kelly quitting, administration officials said. Mr. Trump has told these aides that he is resigned to the possibility of Mr. Kelly leaving, and that he probably will replace Mr. Kelly with Nick Ayers, who is currently chief of staff to Vice President Mike Pence.

At the White House Tuesday afternoon, Mr. Trump declined to say whether he planned to fire Ms. Nielsen or make other staff changes. “We’ll be talking about it,” he told reporters when asked about his plans.

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White House officials also cautioned that Mr. Trump, who forced out Attorney General Jeff Sessions last week, has considered changes to the administration in the past. The president often games out multiple staffing scenarios with advisers, including months of talking about whether to replace Mr. Kelly. While those discussions often signal impending changes, that is not always the case.

“This is how the president works,” one White House official said. “He’s doused a bunch of people in gasoline and he’s waiting for someone to light a match.”

A White House spokeswoman declined to comment. A spokesman for the Homeland Security Department also declined comment.

Mr. Trump has already decided to remove Ms. Ricardel, the top deputy for national security adviser John Bolton, officials said on Tuesday.

A rift emerged after Mrs. Trump staff’s battled with Ms. Ricardel during the first lady’s trip to Africa last month over seating on the plane and requests to use National Security Council resources, according to people familiar with the matter. The first lady’s team also told Mr. Trump that they suspect Ms. Ricardel is behind some negative stories about Mrs. Trump and her staff.

The first lady’s office issued a statement on Tuesday calling for Ms. Ricardel to be dismissed. “It is the position of the Office of the First Lady that she no longer deserves the honor of serving in this White House,” said Stephanie Grisham, a spokeswoman for Mrs. Trump.

Late Tuesday, one White House official pushed back against the criticism but offered no assurances about Ms. Ricardel’s job security.

“Mira Ricardel is one of the highest ranking women in the Trump administration,” the official said. And she “has never met the first lady.”

Ms. Ricardel also repeatedly clashed with Defense Secretary Jim Mattis and his Pentagon team over staffing decisions and policy differences, according to people familiar with the feud.

A National Security Council spokeswoman declined to comment on the activities of Ms. Ricardel.

Ms. Ricardel has served as a vital ally for Mr. Bolton since he took the national security job in April. He resisted efforts by Mr. Kelly to force her out, including when the chief of staff cited Mrs. Trump’s concerns two weeks ago, the officials said. Mrs. Trump and her staff then discussed the issue with the president during the trip to Paris, White House officials said. Mr. Trump told his wife that he would have Ms. Ricardel removed, the officials said.

Mr. Bolton, meanwhile, has been among those pushing for Ms. Nielsen’s ouster, officials said. The Washington Post reported Mr. Trump’s decision to remove Ms. Nielsen on Monday.

Ms. Nielsen’s removal hasn’t been finalized, and her ouster has been a constant topic of discussion for Mr. Trump and top aides, White House officials said. They also cautioned that it was unclear when, or whether, she would leave.

One reason: The White House has no one ready to nominate, and there are succession questions at Homeland Security. The administration has yet to replace Elaine Duke, who resigned as the deputy secretary in February. The third in line at DHS is Claire Grady, the undersecretary for Management. White House officials have told Mr. Trump she doesn’t have the leadership experience to take over DHS.

Mr. Trump also has soured on Kevin McAleenan, who is commissioner of U.S. Customs and Border Protection, and Brock Long, head of the Federal Emergency Management Administration. The latter has been under investigation by the agency’s inspector general.

One source of tension between Mr. Bolton and Ms. Nielsen stemmed from a plan she raised to deal with the migrant caravan heading to the U.S.-Mexico border. Ms. Nielsen raised the possibility of asking the United Nations refugee agency to set up camps on the Mexico side of the border to house the migrants, said to people familiar with the talks.

Mr. Bolton pointedly dismissed the idea as unworkable and misguided, a response that irked Ms. Nielsen and triggered a forceful defense from Mr. Kelly, these people said. Mr. Kelly asked Mr. Bolton what he thought would be a better approach, and Mr. Bolton said he would discuss it directly with the president, one of these people said.

In a meeting in the Oval Office, Mr. Trump further aggravated Mr. Kelly by suggesting that Jared Kushner, the president’s son-in-law and top adviser, use his contacts in the Mexican government to try to resolve the caravan issue. “Let’s get Jared involved; he’s our best guy on this,” Mr. Trump said.

In recent days, Mr. Trump referred to Mr. Ayers in the present tense as his chief of staff, one White House official said. Mr. Trump has told officials he expects to offer Mr. Ayers the job when Mr. Kelly leaves. Mr. Ayers declined to comment.

But there remains significant opposition among Trump advisers to installing Mr. Ayers, White House officials said. On the flight from Paris to Washington on Sunday, several top aides urged Mr. Trump not to choose Mr. Ayers.

The relationship between the president and Mr. Kelly has suffered a series of twists and turns over the past year and a half, including a high point in July, when Mr. Trump asked Mr. Kelly to remain in the job until the 2020 re-election campaign, and he agreed to do so.

—Peter Nicholas

contributed to this article.

Corrections & Amplifications

White House Deputy National Security Adviser Mira Ricardel is expected to be fired. An earlier headline incorrectly said she already had been fired and escorted from the White House. Also, Ms. Ricardel is the top deputy for national-security adviser John Bolton. An earlier version of this article incorrectly spelled her last name as “Ricadel” in one instance. (Nov. 13)

Write to Michael C. Bender at Mike.Bender@wsj.com and Dion Nissenbaum at dion.nissenbaum@wsj.com