Activist hedge fund Elliott Management thinks Walmart, Google or several private equity firms would be interested in acquiring eBay's marketplace business if it sheds StubHub and eBay Classifieds Group, according to a person familiar with the matter.

Elliott disclosed it owns more than 4 percent of eBay in a letter Tuesday, which also outlined recommendations for the company, including spinning off StubHub and eBay's portfolio of classified advertising properties. Activist hedge fund Starboard Value LP also has taken a position in eBay and plans to speak to the company about similar changes, said another person familiar with the matter.

EBay has a market valuation of more than $31 billion. If eBay is able to separate StubHub and the classifieds business, the remaining marketplace business could be a more realistic size for a private equity transaction. EBay's marketplace business generated $2.1 billion of revenue in the third quarter. StubHub took in $291 million in sales and the classifieds unit booked $254 million.

Elliott projects the Classifieds Group could sell for between $8 billion and $12 billion and estimates StubHub could fetch between $3.5 billion and $4.5 billion. If EBay sells the marketplace business without operational improvements, Elliott projects it could fetch about $15 billion, one of the people said.

Founded in 1995 before the first dot-com boom, eBay was once the mecca of online e-commerce but has long since handed that mantle over to Amazon. Elliott said the company's share price could reach more than $63 a share by 2020 if it follows its plan to focus on the "deeply undervalued" marketplace business.

Spokespeople for Google and Walmart didn't immediately respond to requests for comment. eBay responded to the Elliott letter in a statement, saying the company appreciates "Elliott's recognition of the strength and power of eBay's business and will carefully review and evaluate Elliott's proposals."

EBay has steadily grown revenue since splitting off PayPal in 2015. Still, shares are about flat compared to where they were two years ago. The S&P 500 is up about 15 percent over the same time period.

This isn't the first time eBay has dealt with activists. EBay settled a proxy fight with activist investor Carl Icahn in 2014 after he called for the company to spin off PayPal. The company ended up taking Icahn's advice about a year later.

Ebay shares were up more than 6 percent on the news of the Elliott stake in late Tuesday trading, a down day for most of the rest of the tech market.

Thomas Franck contributed to this report.

WATCH: Elliott Management takes $1.4 billion stake in eBay