Discussions are understood to be continuing between the two firms, however it is believed that no purchase is imminent.
Analysts say a deal is unlikely unless increases its estimated $1bn offer, or if there were a change in business conditions.
Speaking to Reuters, Scott Kessler, an analyst with S&P's equity research services, said: "We think Yahoo! is being out-executed by Google in terms of innovation, financials and partnerships/acquisitions.
"With its shares close to their 52-week low, we believe the pressure is significant for Yahoo! to do something meaningful to garner positive interest and restore investor confidence."
was set up for college students in February 2004 and allows users to create web pages with their own profiles, look for friends and send messages to each other. It has more than 9m users.
Earlier this month, Sumner Redstone, chairman of MTV-owner Viacom, said the company would not attempt to acquire the site because it is too expensive.
Microsoft has also been named among the firms that have held talks about acquiring the social networking site.
The $1bn price tag on the business is almost double the $530m News Corp paid for , and it is the success of the site that has pushed the anticipated price for Facebook much higher.
This week, Google agreed to buy video-sharing network , ending months of speculation.
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