TechCrunch’s article by Michael Arrington said the two companies are also considering working together on a Google real time search engine.
Google would pay for Twitter in cash or stock or a combination of the two, the website reported.
Industry experts say Arrington has a mixed record but was the first to report the rumor that Google would buy video-sharing site YouTube in late 2006.
Arrington said the talks were "fairly early stage."
A Google spokesman in London told Reuters the company did not comment on rumors or speculation. A spokesperson for Twitter could not be reached immediately.
San Francisco, California-based Twitter has enjoyed a surge in popularity since its creation three years ago, despite the fact that the company has yet to make any money.
Twitter’s co-founder Biz Stone said in March that the company was eager to partner with other companies, including Google, but was not considering a merger or buyout.