Alwaleed is a closely watched figure in international markets because of successful investments through Kingdom Holding in companies such as Citigroup and Rupert Murdoch's News Corp.
Twitter has filed for an initial public offer of shares with U.S. regulators, the company said on Thursday, taking a first step toward what would be Silicon Valley's most anticipated debut since Facebook listing last year.
"With the 300 million customers they have and half a billion tweets a day, the growth potential is tremendous," Alwaleed said. He said Chief Executive Dick Costolo was "very knowledgeable, very much trustworthy".
The market expects the company's value once listed to be more than $10 billion; Alwaleed sees potential for a much higher valuation.
(Read more: Twitter files for long-awaited IPO)
"We hear that the company is valued at $14 billion-$15 billion but there have been trades above this valuation. We believe it might be worth more than that."
Facebook's rocky 2012 debut and subsequent share-price plunge chilled the consumer-dotcom IPO market for a year. The stock clawed its way back to its $38 IPO price in July, however, and is now at a record high after touching $45 this week.
Alwaleed wouldn't comment on whether Twitter would choose to list on the New York Stock Exchange in order to avoid Facebook's disappointing experience on Nasdaq.
But the prince said: "In my discussion with Mr Costolo and the management of Twitter, I cautioned them to be very careful and not to repeat the mistakes of Facebook.
"The lessons are not to brag too much, don't be greedy - I mean price it right and be realistic."
(Read more: Twitter IPO interesting at right price)
He added, "There could be a good surprise for the market, where Twitter revenues coming from mobile compared to fixed devices are way ahead of what Facebook came with at the time of the IPO."
By transmitting news and opinion, social media such as Twitter played a big role in mass protests that have led to the ousting of Arab rulers in Tunisia, Egypt, Libya and Yemen since 2011.
Saudi Arabia, where Twitter use has been growing rapidly, has spent billions of dollars on welfare schemes to contain discontent and avoid unrest.
Alwaleed said on Sunday, "There is no doubt that Twitter accelerated the process of disseminating news. It has to remain an open forum for everyone."
(Read more: Twitter is going public, and its stock ticker symbol is...)
He added, "I'm totally against anybody who tries to control or censor Twitter or any other social media, even if it is governments. It's a losing war."