Both companies have refused to comment on the speculation, but talks are thought to be nearing a critical stage.
A decision is expected within the next few weeks, according to reports on Reuters.
StumbleUpon uses recommendations from its 2.3 million users to match websites, videos and photos to a user's interests.
Users can cast their votes using a browser toolbar, giving sites the thumbs up or thumbs down.
"StumbleUpon learns what you like and makes better recommendations," the website claims.
EBay has made a number of high-profile acquisitions in its history, including the US$1.5 billion buyout of PayPal in July 2002 and the US$2.6 billion deal for Skype in September 2005.
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