Big changes may be coming for Yahoo. A report from The Wall Street Journal says that Yahoo’s board may consider a proposal to sell the company’s core business – the search and advertising sections of the 20-year-old company that have struggled to compete with Google and Facebook, in the face of shifting consumer tastes.

A Yahoo spokeswoman declined to comment on the report.

The possible move brings sharp scrutiny to Yahoo chief executive Marissa Mayer, who was brought on three years ago to effect a turnaround at a company. At that time she was Yahoo’s fifth chief executive in five years, and cast as a savior for the firm, which had struggled to find a strategy to stem its losses.

Back then, Yahoo was facing a key problem: It was losing users. The company had been focused on the desktop Web – where its market share in search was shrinking. Today it is still well behind its rivals. In October, comScore reported Yahoo had a 12.6 percent share of the desktop search market, placing it behind Google’s 63.9 percent and Microsoft’s 20.7 percent for Bing.

Meanwhile, even as Yahoo has struggled to stem the losses on desktop, consumers have started shifting the bulk of their searches to the mobile platform, where Google and Facebook are even more dominant. Mayer’s initial strategy was to acquire several mobile-focused startups while striking deals to increase Yahoo’s search footprint. She also built up the company’s focus on producing its own content, hiring Katie Couric to anchor a news team. Yet while Mayer has managed to stabilize Yahoo’s business – and even making some money off of mobile ads – she hasn’t managed to kickstart another period of growth.

Investors have clearly been running out of patience, with some suggesting Yahoo consider a merger with AOL. Calls for change grew louder after another lackluster earnings report in October. Last month, investors from Starboard Value called on Yahoo to stop a planned spin-off of its high-value stake in Alibaba, the Chinese Internet firm, as part of an effort to avoid heavy taxes. The value of those Alibaba shares are estimated to be worth as much as $32 billion. Meanwhile, Yahoo’s total market value is around $34 billion.

In many ways, Yahoo’s future depends on finding the best way to lower its tax bill as it considers what to do with such a valuable stake.

The tech giant would face capital gains taxes if it simply sold its shares in Alibaba. And while Yahoo has said it would like to spin off its 15 percent stake in the Chinese retailer into a new company, it is also unclear whether that would draw a hefty tax bill.

The Internal Revenue Service has not ruled on the issue, and Yahoo could be hit with a $9 billion tax bill, said Robert Willens, an independent tax consultant. “I think the spinoff would qualify for tax-free treatment, it meets all the requirements,” he said.

But the risk of a multibillion tax hit has some Yahoo shareholders asking the company to abandon its plans.

“If you stay on the current path, we believe the potential penalty for being wrong is just too great, and the potential reward for being right is not materially better than the alternative,” Starboard Value, a New York-based investment firm, said in a November letter to the company.

Instead, Starboard says Yahoo should sell its core Internet search and advertising business. The remaining company would include the stake in Alibaba and Yahoo Japan, which is worth as much as $8.5 billion. The proposal would also not be as costly.