The blog Techcrunch reported that Google and Twitter are in late-stage acquisition talks, which could lead to a sale.
No sale price has been cited, but whatever the price it is likely to be considerably higher than the $250m it is currently valued at and the $500m Twitter turned down from Facebook in November 2008.
Any deal with Google would likely involve cash and stock. Facebook offered Twitter $500m (£330m) in stock, but the two disagreed over the social networking site's valuation. Unlike Facebook, Google is publicly quoted and there would be no disagreement about the value of its stock.
When Twitter turned down the Facebook deal, co-founder Biz Stone said that the company wanted to remain independent to expand on "its messaging service and try their hands at building a functioning revenue model".
The rumour that Google is in talks to buy Twitter follows a report last month that Amazon might also bid for Twitter.
The combination of Google and Twitter is one that holds considerable logic, according to industry analysts, as it would give the search giant a major asset in what is seen as the next big thing in digital media - the real-time web and particularly real-time search where some see Twitter's value lying.
"We've been arguing for some time that Twitter's real value is in search. It holds the keys to the best real-time database and search engine on the internet, and Google doesn't even have a horse in the game," Techcrunch said.
Twitter's power in the search market has grown exponentially over the last year since it acquired the search engine search.twitter.com, last summer.
It has become invaluable tool for those working in branding, marketing and communications as it allows people to search for real-time brand feedback on what consumers are saying.
Todd Chaffee, from Institutional Venture Partners and one of Twitter's new backers, said recently: "You put a question out to the global mind, and it comes back. Millions of people are contributing to the knowledge base. The engine is alive. You get feedback in real time from people, not just documents."
It is real-time search where Chaffee and Twitter itself increasingly see its commercial future and not in charging businesses or others to use the micro-blogging service.
As part of the deal Techcrunch says that "the two companies are also considering working together on a Google real-time search engine".
Elsewhere it has been reported that Twitter is working with Google to sell ads.
Google has started offering marketers the ability to stream their five most recent Twitter messages or "tweets" across the Google AdSense network.
It has already signed up Intuit, which is using it for its TurboTax brand in an attempt to attract more Twitter followers [@turbotax].
Seth Greenberg, director of marketing at Intuit, said: "We could have used this as an acquisition vehicle, but we're looking at it more like a conversational vehicle. We're not going to hard sell you on the product, but we want people to know there are lots of people here who can help answer your questions."
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