The two companies have been in talks for a month, the person said, but cautioned that there is no guarantee a deal will be reached.
Numerous discussions have been held in recent years about a deal for Alibaba to reclaim some or all of the 40 percent stake in the company that Yahoo acquired in 2005.
A $17 billion tax-free asset swap between the two companies fell apart in February.
The latest deal would not be tax-free and would be much more straightforward, the source told Reuters on Friday.
The overall complexity of this deal is much simpler. There's no [Internal Revenue Service] risk, there's no complications with regards to the identification of assets, the source said. In a best-case scenario, a deal could be weeks away, the source said.
The situation may have become more complicated following Thursday's revelation that Yahoo CEO Scott Thompson's resume falsely stated that he had earned a computer-science degree in college.
Yahoo initially called it an inadvertent error, but the company has since said its board is reviewing the matter. Activist investor Third Point, which is leading a proxy fight against Yahoo's board of directors and which discovered the error in Thompson's resume, has demanded that Yahoo fire Thompson by Monday.
Yahoo and Alibaba declined to comment.
Yahoo acknowledged that it was in talks with Alibaba, during its first-quarter earnings conference call with analysts last month. During the call, Thompson said the two companies were working on a simplified transaction to monetize a portion of Yahoo's stake in Alibaba.
To fund the deal, Alibaba would raise capital. The valuation that Alibaba receives in the fundraising will determine how much Yahoo earns in the transaction, the source said.
In September, Alibaba was valued at $32 billion when Silver Lake and other firms invested in the company, according to media reports at the time. At that valuation, Yahoo could make between $4.8 billion and $8.0 billion by selling from 15 percent to 25 percent of Alibaba.
Of all the previous ones we've worked on, this one feels like it might actually have a chance of getting done. Or at least it did until a day and a half ago, the source said, referring to the controversy around Thompson's resume.
Details of the talks were first reported by the Wall Street Journal on Friday.
(Reporting by Alexei Oreskovic; Editing by Richard Chang)