“This is a fantastic opportunity for someone who’s wired for problem solving and wants to make their mark by turning around the image of the company,” said Jason Hanold, managing partner at Hanold Associates, a boutique executive search firm. “Yes, they’re inheriting Uber’s entire toxic culture. But they’re also getting thousands of employees who are hungry to change it.”

The chance of having an impact is high. Apart from the opportunity to steer a turnaround, any chief executive would be walking into a company that has already reached enormous scale. As a result, changes made by a new chief would affect millions of people globally, not to mention Uber’s work force of more than 15,000 employees and hundreds of thousands of contract drivers.

The eventual chief executive would also have the opportunity to take Uber public. The company, which began in 2009, is now the highest-valued private company in the world, with a valuation of around $70 billion. And while Uber is unprofitable, its revenue has been growing. That would make an initial public offering a huge event on Wall Street, as well as for Silicon Valley investors who have billions of dollars wagered on Uber’s success.

For now, Uber’s executive search committee, which includes five members of its board, has kept the lid tight on the list of candidates. After a torrent of leaks before Mr. Kalanick’s departure, two of the people familiar with the search said there has been a renewed effort to keep quiet.

Among those up for consideration have been Susan Wojcicki, who leads YouTube. Others include Adam Bain, Twitter’s former chief operating officer; David Cush, a former chief executive at Virgin America; the former Yahoo chief executive Marissa Mayer; and Thomas Staggs, a former chief operating officer at Disney, according to three other people familiar with the search. It was unclear what level of interest, if any, these executives had expressed in the Uber job.