"We think there's a good chance he's not there within a year," Peck said.
Contrary to widespread expectations that Twitter's CFO Anthony Noto might take the CEO position, Peck said there are "a lot of interesting candidates out there" and "coupling (Noto) with a large media personality ... would be received very well."
Twitter did not immediately respond to a CNBC request for comment.
The analyst's call is one of several big predictions he's making for the Internet tech stocks in 2015.
"We think this is the year we're going to see a lot more of the Asian companies coming abroad and coming into the U.S.," Peck said.
Most notably, Alibaba has taken stakes in U.S. start-ups Tango and ShopRunner. "The U.S. is in their global plans—they're very clear about that. The question is how they enter the market," Peck said. That might involve a partnership or acquisition of major U.S. Internet names such as eBay or Yelp.
He said the next Alibaba "could reside in India."
—CNBC's Katie Young contributed to this report.