In an interview with the British business daily published over the weekend, co-founder Biz Stone said Twitter wanted to become not just a popular site but a viable business, rather than be taken over by another company.
"We’ve created something that people are finding value in," he said. "But we haven’t yet created a business out of this, and we really wanted to do that."
According to the Financial Times, Facebook CEO and co-founder Mark Zuckerberg offered $500 million in Facebook stock for Twitter.
But Stone said Facebook had nothing that Twitter's three co-founders -- Stone, Evan Williams and Jack Dorsey -- wanted.
The daily added, without elaboration, that Twitter still isn't turning a profit more than four years after it was created.
In mid-December, Twitter said it had received a major infusion of funds from a group of investors, which reportedly put a $3.7 billion value on the site.
Created in 2006 to exchange messages of no more than 140 characters, Twitter had 175 million registered users as of November 1, and transmitted 25 billion "tweets" last year. About 95 million messages a day are sent over the site.
It has pursued rapid growth over profits, but since last spring, it has brought in advertising revenues through paid for "promoted tweets."