SAN FRANCISCO — The board of Yahoo will discuss potentially selling off the beleaguered Internet company’s core business during a series of meetings this week, people briefed on the plans said on Tuesday.

Directors of the company will also discuss whether to move forward with plans to spin off Yahoo’s 15 percent stake in the Alibaba Group, the Chinese e-commerce giant. The board will weigh all its options, and it is unclear whether the directors will change course, said the people, who spoke on the condition of anonymity because they were not authorized to publicly discuss the plans.

Still, the discussions — which will take place at a regularly scheduled board meeting — highlight the difficulties that have long troubled one of the most prominent Internet companies.

The discussions are also sure to put attention squarely on Marissa Mayer, Yahoo’s chief executive, and the company’s direction under her leadership. Although Ms. Mayer is credited with stabilizing the company, which was in rapid decline, Yahoo has introduced no breakthrough products during her three years at the helm and has fallen further and further behind competitors like Facebook and Google in the battle for advertising dollars.