Yahoo is weighing a sale of its core Internet business and will not sell its stake in Chinese e-commerce firm Alibaba Group Holding Ltd, CNBC reported, with an announcement as soon as Wednesday.

The moves represent a stark rejection of CEO Marissa Mayer's plan to sell the $30 billion Alibaba stake, and revive the core Internet unit focusing on mobile, video and social media ads.

Yahoo shares rose more than 2 percent in after-hours trading. Alibaba's shares rose 1.3 percent.

Yahoo's core business consists of selling search and display ads on its popular news and sports sites, e-mail service and products like Tumblr.

Yahoo is also considering what to do with its stake in Yahoo Japan. Yahoo owns 35 percent of that company, worth about $24 billion.

The CNBC report, which cited unnamed sources, did not disclose a possible sale price for the Internet unit. Analysts and bankers have estimated it could get between $2 billion and $8 billion, with many seeing $4 billion as the likely price, but some regard its value as less than zero.

After such a sale, all that would be left, essentially, is the Alibaba and Yahoo Japan stakes.

Private equity, media and Internet firms are potential buyers. On Monday, the Verizon Communications Inc CFO said that the No. 1 US wireless carrier could look at buying Yahoo's core business.

The latest report came after a three-day meeting of Yahoo's board of directors last week, which concluded on Dec 4. Yahoo has faced pressure from activist investor Starboard Value LP to sell the core business rather than proceed with the planned spin-off of its Alibaba stake, which could trigger large tax payments.