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While private-equity firms have long contemplated a deal for Yahoo, talks have heated up in recent weeks as several senior Yahoo employees have left the company, intensifying pressure on Yahoo Chief Executive Carol Bartz to prove she can turn the company around, the people familiar with the matter said.

Ms. Bartz has improved Yahoo’s profitability by cutting costs, but revenue hasn’t grown much and the company faces other problems. The Internet pioneer, for example, has shown fewer benefits than competitors from a broad recovery in display advertising—an area where it faces increasing competition from Google and Facebook Inc.

The company, which reports third-quarter earnings next week, claims that more than 600 million people use its home page, email service or other sites every month. But the number of Yahoo pages viewed by its users, known as “user engagement,” began shrinking in the second quarter. Yahoo also has seen a drop in the value of advertising against content that Yahoo pulls from other sources.

Ms. Bartz said in a recent interview she needed more time to pull off a turnaround.