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Yahoo CEO Marissa Mayer acknowledged the letter Friday evening.
"As part of our regular evaluation of Yahoo's strategic initiatives to drive sustainable shareholder value, we will review Starboard's letter carefully and look forward to discussing it with them," she said, in a statement.
Starboard, which recently went after Darden for wasting money at its Olive Garden restaurants, said a tie-up between Yahoo and AOL could "offer synergies of up to $1 billion" and reduce corporate overhead cost.
Starboard said it had acquired a significant stake in Yahoo, adding that a possible AOL deal, along with other recommendations, would unlock tremendous value for shareholders.
AOL shares jumped as much as 6 percent after the news before easing, while Yahoo rose about 4 percent.
"[W]e believe a merger of AOL and Yahoo's core business may be one of the best ways to both fully seize the cost reduction opportunity and also to tax efficiently monetize Yahoo's noncore equity holdings, " the letter said.
Starboard said the deal could help the companies navigate the ongoing industry changes, such as the growth of programmatic advertising and migration to mobile.
The letter, which was signed by Starboard CEO Jeffrey Smith, described Yahoo as "deeply undervalued relative to the sum of its parts" and said the company must take immediate steps to "remedy this valuation discrepancy."
Starboard pointed to a valuation gap of about $11 billion.
"The core problem for Yahoo, outside of Alibaba, is they don't really have an exciting story, " said Gene Munster, an analyst at Piper Jaffray. "If they could use acquisitions as a way to drum up some excitement in a longer-term business I think that most investors would look upon that favorably."
Munster, who has a $48 share price target on the stock, said a potential AOL acquisition would add to Yahoo's financial value, but it wouldn't solve Yahoo's core issue: user growth. "AOL is a fading giant as is Yahoo ... the combination of that doesn't add excitement that new users are going to come to," he said.
Instead he said he believes Yahoo should should explore acquiring "something on the content angle."
While the proposed tie-up with AOL may not be "sexy," there are a lot of reasons to think a combined company would work, said Colin Gillis, analyst at BGC Partners.
For one thing, AOL would bring original video and original content that Yahoo has been openly seeking, Gillis said.
There's enough overlap that possibly significant cost savings could be found. And Yahoo clearly needs help gaining market share in the "raging bull market for online advertising," Gillis said.
Yahoo currently has a market valuation of $40 billion, in comparison to industry leader Google's nearly $200 billion market cap.
This is not the company's first encounter with a high-profile hedge fund. In 2012, activist investor Daniel Loeb sent a letter to Yahoo's board demanding that its then-CEO Scott Thompson be fired.
Loeb was a primary player in recruiting Mayer as Thompson's successor, but the two reportedly had major differences in opinion about Yahoo's strategy going forward, which eventually lead to Loeb's departure from the board, the New York Post reported last year.
AOL declined to discuss the matter, while Yahoo did not respond to CNBC's request for comment.
—CNBC's Matt Hunter contributed to this report.
Disclosure: CNBC has a content sharing partnership with Yahoo's finance site.