The newspaper, citing two people briefed on the matter, said the popular website is in the process of raising $400 million in a deal that has provided the latest estimation of its value.
The Wall Street Journal had reported a similar deal on Tuesday, putting the company's valuation at up to $7 billion.
The Times cited one of its sources as saying that the financing round will be led by DST Global, the investment firm headed by Russian billionaire Yuri Milner, and that previous investors, including the venture capital firm Kleiner Perkins Caufield & Byers, will also participate.
In December, Twitter received an injection of $200 million from investors to help fuel its growth, reportedly giving the San Francisco-based company a valuation of $3.7 billion.
That round of financing was led by Kleiner Perkins Caufield & Byers.
Twitter has fended off several buyers and has repeatedly said it is not considering going public.
Founded in 2006, the company recently announced that Twitter users are sending 200 million tweets a day, up from 65 million a year ago.
A recent study by the Pew Research Center said 13 percent of online US adults use Twitter, up from eight percent in November 2010. The site has more than 200 million total users.