Yahoo CEO Marissa Mayer has repeatedly preached that it will take time for her to turn the company around.

But analysts and investors are increasingly reluctant to give her more time and are even speculating about whether she should (or will) be fired sometime soon.

Shares of Yahoo (YHOO) have plunged nearly 35% this year and many on Wall Street are tired of hearing that Yahoo is a turnaround story. They want results.

SunTrust Robinson Humphrey analyst Robert Peck wrote in a report Monday morning that his clients have been asking him a lot about Mayer, especially since many Yahoo senior executives have left the company in the past few months.

This Yahoo "brain drain" has some investors worried that Mayer is managing a sinking ship.

"With the recent turnover in top level executives, some have questioned whether the CEO's position is stable," Peck wrote.

Related: Mayer not worried about executive exodus at Yahoo

But Peck took it one step further.

"We held many conversations with leading industry participants and investors to gauge what attributes would be needed and who would be a strong potential CEO candidate, should the company ultimately decide to make a change," he wrote.

Some of the top candidates on this wish list?

• Ross Levinsohn -- a former interim Yahoo CEO and current CEO of Scout Media
• Dan Rosensweig --a former Yahoo COO and current CEO of online textbook seller Chegg (CHGG)
• Jim Lanzone -- CEO of the digital unit of CBS (CBS) and former CEO of IAC (IACI)-owned Ask.com
• David Rosenblatt -- former CEO of online ad firm DoubleClick and current CEO of online luxury retailer 1stdibs
• Sheryl Sandberg -- Facebook (FB) COO

Peck felt that Levinsohn and Rosensweig would be the most likely candidates given their past experience with Yahoo.

But if Yahoo were to part with Mayer, investors may want someone who has more of a fresh perspective.

Ironically enough, Mayer was thought to be that person when Yahoo hired her away from Google (GOOGL) more than three years ago.

And interestingly, several candidates cited by Peck also have Google ties.

Related: Marissa Mayer STILL hasn't fixed Yahoo

DoubleClick was bought by Google in 2008 and Rosenblatt continued to work at Google for a year after the DoubleClick acquisition.

Sandberg was a Google executive before she joined Facebook.

And two other people cited by Peck as possible Mayer replacements also now work for Google: YouTube CEO Susan Wojcicki and Margo Georgiadis, president of ad sales and operations for Google's North American and Latin American units.

Still, is Mayer's job really in jeopardy?

NYU Stern School of Business marketing professor Scott Galloway told Bloomberg in September that Mayer is the most "overpaid CEO in history" and that she still has her job only because she is pregnant. (Mayer is expecting identical twin girls in December.)

Those provocative comments surprisingly did not cause as big of a backlash as you might have expected though.

And it's likely because Yahoo has continued to struggle to turn itself around.

Shares fell 5% the day after the company's third-quarter earnings disappointed Wall Street.

Peck wrote in a report earlier this month that unless Mayer has the support of senior executives, employees, partners, and investors, then "a seamless transition to new leadership could be in the best interest of the company and shareholders."

One of those shareholders -- Starboard Value's managing member Jeffrey Smith -- has been extremely critical of Mayer and Yahoo's board as well.

Smith wrote a letter to Mayer and Yahoo chairman Maynard Webb earlier this month and asked for the company to try and sell off its core search and display advertising assets instead of spinning off its stake in Chinese online retailer Alibaba (BABA).

Smith also appeared to suggest that Yahoo will never be able to turn around the core assets under Mayer's leadership.

He wrote that the value of Yahoo is likely to decline further "without significant change to the culture" and added that "we cannot imagine that any prudent individual assigns a high probability that Yahoo is on a path to substantially increase" its profits.

Related: Yahoo will spin off Alibaba stake no matter what IRS says

But it's not clear who would want to buy Yahoo.

AOL was once thought to be a logical candidate for a merger. But Verizon (VZ) scooped up AOL earlier this year. It seems unlikely that another major media company would want Yahoo at this point.

Yahoo continues to lag Facebook and Google in the digital ad race. Twitter (TWTR), despite its troubles, is still expected to gain market share while Yahoo steadily loses it, according to figures from eMarketer.

That means Mayer will likely have no choice but to stick with the plan to spin off Alibaba, even though Wall Street no longer thinks it can significantly boost the company's fortunes.

For one, it remains uncertain if the IRS will rule that the Alibaba spin-off will be tax free.

What's more, the value of Yahoo's Alibaba stake has plunged this year. Shares of Alibaba are down 20% due to concerns about the Chinese economy, increased competition and pirated goods on Alibaba sites.

Yahoo had no comment for this story. And to be sure, there are no rumors whatsoever that Mayer is on the way out.

But if the calls for Mayer's ouster grow louder and more frequent, then Yahoo's board may not be able to ignore them indefinitely.

Just look at what happened to Mayer's numerous predecessors. Terry Semel, Jerry Yang, Carol Bartz and Scott Thompson didn't leave on the best of terms.

It seems that the only constant for Yahoo over the past 15 years is that investors are never happy with the CEO.