Wanted: a seasoned executive to take the top position at a troubled technology start-up. Must be willing to fix a broken culture, deal with an aggressive predecessor, battle a risky lawsuit and prepare the company for an initial public offering. Self-starters preferred.

This is essentially the pitch that Uber is making to potential chief executive candidates after Travis Kalanick, the ride-hailing company's co-founder, was ousted from the top spot last month. By some accounts, the job appears to be a thankless one at a company whose reputation is in the toilet. So who would want it?

Quite a few people, as it turns out.

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Despite a series of scandals that have rocked Uber to its core this year, competition for the chief executive position is robust, according to people familiar with the search who asked to remain anonymous because the process is confidential. The company has received a flood of interest since Mr. Kalanick vacated his seat in June, and Uber's board has interviewed multiple candidates.

For those applicants, the calculus is easy. Despite Uber's problems, executives see an opportunity to shepherd the company — which operates in more than 80 countries and pulls in billions of dollars each quarter — through the most trying time in its eight-year history.

"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.

Others, like the former Google sales executive Nikesh Arora, have been quietly advancing themselves for the position, according to two of the people.

Mr. Bain, Mr. Cush, Ms. Mayer, Mr. Staggs and Mr. Arora did not immediately respond to requests for comment. A YouTube spokesman declined to comment about Ms. Wojcicki.

Some candidates have expressed concern over how Uber's board operates, especially because Mr. Kalanick retains a seat. Mr. Kalanick, who remains a significant Uber shareholder, has been active in the search for his replacement, according to two of the people familiar with the candidates, although the candidates have been assured that they would have autonomy as chief executive.

Uber has other considerations in choosing a new leader. The company has faced intense criticism for its lack of diversity and has only recently begun to address the matter. Last year, Arianna Huffington, the media entrepreneur who runs the health and wellness business Thrive Global, joined Uber's board, and in the past few months the company has recruited female and minority executives.

For the eventual winning candidate, there will be plenty of difficulties. Negative perception of Uber tripled, to 27 percent of respondents, in a survey conducted in May by cg42, a management consulting firm. The company has had a more difficult time hiring technical talent in light of its negative image.

Uber also faces a lawsuit filed by Waymo, the self-driving car company spun out of Google, over claims of stolen trade secrets. And Uber is in the midst of reforming its fractured culture after a former employee spoke publicly about sexual harassment at the company.

While the job will make Uber's next chief executive wealthy, it will not necessarily make him filthy rich: With the company's valuation already so high, any stock doled out to a new chief would most likely have to experience an enormous rise in value after a public offering for the returns to be considerable.

Yet the positives of the job still outweigh the negatives for hopeful applicants.

"Even with all the problems that companies like Uber have, there will always be top candidates who want to go there," Mr. Hanold said. "These people are problem solvers: The hairier a scenario is, the more they're attracted to trying to fix it."