Last fall, the nonprofit that controls OpenAI tried to fire the company’s high-profile leader, Sam Altman. It failed.

Ever since then, Mr. Altman has been trying to wrest control of the company away from the nonprofit.

Under the watchful eyes of government regulators, the press and the public, Mr. Altman and his colleagues are working to sever the nonprofit’s control while ensuring that the existing board is properly compensated for the changes, according to four people familiar with the negotiations who spoke on the condition of anonymity.

Mr. Altman and his colleagues need to answer a question: What is a fair price for ceding control over a technology that might change the world? Proper compensation to the nonprofit is still being debated, but it could easily be in the billions of dollars, one person said.

And the clock is ticking for OpenAI’s board of directors. It has promised investors that it will restructure the organization within the next two years, according to documents reviewed by The New York Times.

“We are and have been for a while looking at some changes,” Mr. Altman said this month during an appearance at The Times’s DealBook Summit in New York. “It is, as you can imagine, complicated.”