At the Mobile World Congress in Barcelona, Costolo was asked whether Google was able to afford a $10bn acquisition of Twitter, after talk that the search engine giant was preparing a bid.
"People write that stuff all the time. I don't know where these things come from - it's just a rumour," said Costolo, who took over as chief executive from Twitter co-founder Evan Williams last October.
Costolo said that Twitter would focus on its core mission of "instantly connecting people everywhere to what's most meaningful to them".
He also suggested that the five-year-old company would soon introduce new ways to generate revenue, adding to the already available promotional tweets, accounts and trends. He did not supply any further information on this, though.
Costolo insisted that Twitter is "making money" and now regularly carries 130 million tweets a day, up from 100m at the end of last year. Daily usage peaked in Japan on New Year, when there were 6,000 tweets a second. The recent Superbowl also saw tweets reach 4,000 per second.
"At the end of this year's Superbowl we saw 4,000 tweets per second," Costolo said. "During the game there were sustained periods when it was 3,000 tweets per second. Just to give you some contrast, during the 2008 Superbowl we served 28 tweets per second."
His comments come as online gaming firm Zynga, maker of the popular FarmVille game, has emerged as the next target for private investors.
According to The Wall Street Journal, Zynga is in talks with investors about raising $250m in a deal that would value the three-year-old company at up to $9bn.