Although Alibaba is unlikely to set an IPO price until this summer, analysts estimate the Chinese company's market value at $150 billion to $200 billion. At that level, the 208 million shares that Yahoo is required to sell will bring in at least $10 billion. The Sunnyvale, California, company would still own about 315 million Alibaba shares that it could sell at a later date.
With that much money coming in, Mayer could afford to make a big splash by buying a hot startup such as rising social media star Pinterest or the ephemeral messaging service Snapchat. But those startups still aren't generating much revenue, an issue that would probably rattle investors if Yahoo dared to buy them. What's more, Yahoo could face competition from even richer bidders such as Google and Facebook.
A more logical takeover candidate for Yahoo would be AOL, another once-dominant Internet company that was outwitted by hard-charging innovators such as Google and Facebook, which built lucrative advertising networks around online franchises.
Read MoreYahoo's Mayer: De Castro was not the right fit
Gillis thinks the marriage could make sense for Yahoo because AOL has been more successful in online video—one of Mayer's top priorities—and has done a better job selling ads to other websites. AOL also has a long-running contract to get its search results from Google, an arrangement that might appeal to Mayer because she has publicly expressed disappointment with the revenue that Yahoo has been getting from a similar search deal with Microsoft Corp. If they were combined, Yahoo and AOL also could reduce expenses and make more money by eliminating overlapping jobs and operations.
A potential purchase of AOL got significantly cheaper Wednesday after the company's first-quarter earnings missed analysts' projections. AOL's stock plunged 21 percent, leaving the company with a market value of about $2.8 billion.
There's another reason a deal could come together: Mayer and AOL CEO Tim Armstrong have known each other for years, having both played key roles in Google's success while working at that company. Armstrong specialized in ad sales while Mayer focused more on design and engineering.