Adm. Michael M. Gilday, the chief of naval operations, has indicated that he may reinstate Captain Crozier, who is viewed as a hero by his crew for putting their lives above his career, officials said.

“No final decisions have been made,” Cmdr. Nate Christensen, a spokesman for the admiral, said in a statement on Wednesday to The New York Times. Commander Christensen added that Admiral Gilday was reviewing the findings of a preliminary investigation into the events surrounding Captain Crozier’s removal.

But Admiral Gilday’s decision could be upended by President Trump, who has not been shy about intervening in military personnel cases. Only five months ago, Mr. Trump fired Navy Secretary Richard V. Spencer for opposing the president’s intervention in support of a member of the Navy SEALs accused of murdering a wounded captive with a hunting knife during a deployment to Iraq in 2017.