Who wants to lead the Department of Government Efficiency?

With the departure of Elon Musk and his right-hand man Steve Davis from government, administration officials and members of the controversial cost-cutting effort have been in detailed discussions this week about who will functionally be in charge of it, according to four people familiar with the talks.

Debate about who should take charge has spread through the White House, DOGE and Silicon Valley. In the first days after Mr. Musk’s departure, it centered on the billionaire Joe Gebbia, one of Mr. Musk’s close friends and a board member at his automaker, Tesla.

Mr. Gebbia joined DOGE in February and had been under consideration to effectively take over Mr. Musk’s signature government project, according to a half-dozen people briefed on the conversations. They spoke on the condition of anonymity to disclose private talks.

But Mr. Gebbia, who rose to prominence in Silicon Valley when he co-founded Airbnb, began telling others that he was not interested in a role in which he alone would lead DOGE, according to some of the people. That is in part because of the intense scrutiny that would come with a formal role in charge of it.