According to TechCrunch.com, two sources close to the negotiations confirmed the acquisition talks and said the two companies are considering working together on a 'real time search engine.'
The talks come after previous reports that the popular micro-blogging site refused a 500 million dollar buyout offer from Facebook and raised an additional 35 million dollars in venture capital.
Experts say Twitter poses a threat to Google's dominance in traditional web search and is appealing due to the potential for a real-time search, where a user could get a sense of what is being said about a particular topic instantly.
Google's main headquarters, the Googleplex, is located in Mountain View, Calif. - about 35 miles south of San Francisco.
Twitter co-founders' Evan Williams and Biz Stone have already established a business relationship with Google, selling the free publishing tool, 'Blogger' to the search king.
With just 29 employees, Twitter has seen its Web traffic grow 900 percent over the past year as politicians, business leaders and celebrities have made headlines with their tweets, and Web users from around the world have flocked to the service.