Citing two separate sources, TechCrunch said that the asking price is more than the $250m (£170m) valuation that Twitter's recent round of funding would suggest.
A third source, however, recently added to the TechCrunch report, suggests that talks are only in the early stages.
Twitter has recently reworked its search feature, prompting many to think that this makes the firm more appealing to potential suitors. Search facilities have been added to the 'tweet' pages, and users can search tweets from this view. Twitter claims that the new additions were planned from the start.
Such features would have obvious benefits for marketing and advertising purposes.
"Twitter Search is an engine for discovering what is happening right now," said Twitter co-founder Biz Stone in a blog post.
Stone and co-founder Evan Williams have already sold Blogger.com to Google, and TechCrunch guesses that any deal would involve a straight cash or stock transaction.
Analyst firm Gartner said that a deal makes sense for both firms.
“The culture and ambitions of Twitter and Google match,” Gartner research vice president Jeff Mann noted. “Other tie-ins short of an acquisition could m ake sense, but would be harder to sustain since Twitter already uses such open interfaces. It will be hard to do something that others can't replicate.”
He added that Twitter should look for a buyer now as it is currently at “the top of its hype range” and would otherwise face a long and difficult process of trying to generate revenues as a standalone company.
However, other firms might also be interested in buying Twitter.
"Where's Microsoft in all this? Letting Twitter go to Google only hurts them, badly, in the long-term search game. This is an asset they need to be competing for aggressively," the report said.
Google declined to comment on the reports. In a statement the firm said, "We don't comment on rumour or speculation".
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