The Dow Jones-owned website said Yahoo! is eyeing the move to attract more users from the key 18 to 24-year-old age bracket, and that the Internet pioneer sees Tumblr as one of the "coolest" sites.
The report said talks between the two firms were "serious" but that nothing had been finalized.
Yahoo! has been looking at a range of acquisitions since Marissa Mayer took over as chief executive last year and vowed to revive the company, which has faded in the face of competition from Google.
AllThingsD said Tumblr could fetch as much as $1 billion, and that its current valuation based on investments is believed to be in the range of $800 million.
The report said Tumblr is interested in "strategic" investments, which could mean some kind of alliance.
Yahoo! recently failed in a bid to take over the online video site Dailymotion after the French government, which owns a stake, quashed the deal. The California firm is now reported to be interested in another video website, Hulu.
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