In an interview with Bloomberg, Dorsey reportedly said that Twitter "is not even thinking" about an IPO at the moment.
"A lot of people think of this as a goal you have to get to but it's a milestone," Dorsey told Bloomberg during an interview in New York. "If you think about it as a goal you're rushing towards it and then stop, and that's not the way to build a timeless company."
There's little doubt that a Twitter IPO would be the biggest Internet public offering since Facebook's last year. However, given the poor reception that Facebook's stock has received in the months that followed -- the company will release earnings tomorrow -- it's not known how well Twitter would do as a public company.
Still, Twitter's valuation has continued to climb, with recent estimates pegging it at somewhere in the $9 billion to $11 billion. And the company's investors are no doubt looking to cash out after putting more than a hundred million dollars into the social-networking company.
Though Dorsey is, he's still on its board, and presumably has a good sense of its major strategic plans. Dick Costolo is Twitter's current CEO.
Neither Twitter nor Square immediately responded to a request for comment.