May shared his thoughts after Twitter released second-quarter earnings and revenues that beat Wall Street estimates. The company's stock, however, traded sharply lower following the report's release as CFO Anthony Noto stated there will be a "considerable period of time" before Twitter sees sustained user growth.
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Nevertheless, May said Twitter has at least been able to monetize its existing user base.
"We think, in the U.S., their ad load and their monetization is approaching that of Facebook, which is clearly a much more mature business from an advertising standpoint," he said.
However, Robert W. Baird analyst Colin Sebastian said Twitter investors and management should not get their hopes up.
"One issue I had with the commentary from management last night, despite the fact that they did fess up to some of their headwinds, is that they still characterize the opportunity for Twitter to grow in the same light as Facebook. So investors are still being led down the path that one day Twitter can be as large as Facebook," Sebastian told CNBC's "Squawk Alley" on Wednesday.
Twitter's stock was sharply lower in afternoon trading.
DISCLOSURE: Citi owned at least 1 percent of Twitter's stock when this article was published.