Twitter co-founder Jack Dorsey returned to the role of CEO on a permanent basis this month after the company decided he was the man to turn around its anemic user growth. But Citigroup senior Internet analyst Mark May said Wednesday that may not be the case.

"I think that they have a plan. The problem is it might require a pretty meaningful change to the core experience for Twitter, and that may be something that a founder is unwilling to make," he told CNBC's "Squawk on the Street."