WilmerHale, a prominent U.S. law firm, is close to wrapping up a detailed review of OpenAI’s chief executive, Sam Altman, and his ouster from the artificial intelligence start-up late last year, two people with knowledge of the proceedings said.

The investigation, when complete, could give insight into what went on behind the scenes with Mr. Altman and OpenAI’s former board of directors, which fired him on Nov. 17 before reinstating him five days later. OpenAI, which is valued at more than $80 billion, has led a frenzy over A.I. and could help determine the direction of the transformative technology.

Mr. Altman, 38, has told people in recent weeks that the investigation was nearing a close, the two people with knowledge of the matter said. The results could be delivered to OpenAI’s board as soon as early next month, said the people, who spoke on the condition of anonymity because of nondisclosure agreements.

OpenAI declined to comment. WilmerHale did not respond to a request for comment.

Investigators spent the past three months interviewing OpenAI employees and executives after its former board said it no longer had confidence in Mr. Altman’s ability to run the company, the people said. The board said Mr. Altman had not been “consistently candid in his communications,” though it did not provide specifics.

Privately, the board worried that Mr. Altman was not sharing all his plans to raise money from investors in the Middle East for an A.I. chip project, people with knowledge of the matter have said.

After he was ousted, Mr. Altman waged a bare-knuckle fight against some OpenAI directors to get himself reinstated as chief executive. He won but made concessions. He agreed that OpenAI would hire a law firm to investigate his ouster, and he did not regain his own board seat at the company. But he succeeded in revamping the board, removing two members and adding two others.

OpenAI nearly imploded during the leadership crisis, endangering a potential windfall for its investors, such as Microsoft, and its employees. In the months since Mr. Altman’s reinstatement, insiders have scrambled to contain the fallout, advising employees to keep potential dissent quiet for fear of jeopardizing the company’s fortunes.

OpenAI is considered a leader in generative A.I., technology that can generate text, sounds and images from short prompts. It is also among the many companies aspiring to build artificial general intelligence, or A.G.I., a machine that can do anything the human brain can do.

Meta, Google, Microsoft and others are also racing to develop such technology. Leaders at these companies believe that A.G.I. will revolutionize the computing industry, as well as the global economy and workforces.