Starboard, in September, urged Yahoo to consider merging with AOL on the grounds that a deal could create up to $1 billion (roughly Rs. 6,245 crores) in "synergies" by reducing overlaps in online display advertising and other overhead costs.
The activist-investor holds stake in both companies.
Starboard said in a letter on Thursday that it was "increasingly concerned" by media reports of Yahoo planning acquisitions as it believed the company should first focus on monetizing its investments in Alibaba Group Holding Ltd and Yahoo Japan Corp.
Yahoo holds an approximately 15 percent stake in Alibaba valued at about $39.17 billion (roughly Rs. 2,47,953 crores) as of Wednesday's close and about an $8 billion (roughly Rs. 49,965 crores) stake in Yahoo Japan, as of September 30, 2014.
"A combination with AOL does make sense. They are two laggards who can combine forces and better compete with companies such as Google Inc," B. Riley & Co analyst Sameet Sinha said.
The Starboard letter highlighted reports speculating that Yahoo was considering buying cable assets, including Scripps Networks Interactive Inc and Time Warner's CNN.
Some large shareholders have also reached out directly to Starboard expressing their concern over the media reports, the activist-investor said.
Starboard disclosed a 7.7 million share stake in Yahoo and a 1.9 million share stake in AOL in November.
Yahoo's shares were up 2.4 percent at $49.75, while AOL was up 4.6 percent at $48.27 in afternoon trading on Thursday.
© Thomson Reuters 2015